In this paper, the variational iteration method (VIM) is used to get an approximate solution for a
system of two coupled nonlinear ordinary differential equations which represent the concentrations of carbon
dioxide 퐶푂2 and phenyl glycidyl ether. In this system there are boundary conditions of Dirichlet type and the
other is a mixed set of Neumann and Dirichlet type. Our calculations evidenced by tables and figures for the
analysis of the maximal error remainder values. The variational iteration method gives approximate solutions
with fast convergence. Comparison with the results obtained by the Adomian decomposition method (ADM)
reveals that the numerical solutions obtained by the VIM converge faster than those of Adomian's method. The
software we used in our study of these calculations is Mathematica®
9.
Exact Solutions of Coupled Parallel Resonant Circuits Equations by Decomposit...AI Publications
In this paper, we provide the solution of a modeled parallel resonant circuit using the decomposition method. The parallel resonant circuit also known as resistor (R) in ohms, inductor (L) in Henry and capacitor (C) in farads (RLC) circuit is used in turning radio or audio receivers. The mathematical models are in a system of ordinary differential equations (ODE), which we solve using the Adomian Decomposition Method (ADM). We discovered that this method gave exact solutions as can be obtained using any traditionally known analytic method. These findings are illustrated in three test problems.
A Mathematical Review to Estimate the Fate of a Drug Following Open Two Compa...BRNSS Publication Hub
This paper deals with the application of Laplace Transform [L(f)(s) = F(s) = e-ts f(t)dt] to derive the
formula [(Cp
(t)= Ae-at+ Be-bt] and [Ct
(t)= Te-bt-Te-at] to estimate the fate of a drug in the mammillary body
with the prediction of the biological parameters [k, k12, and k21]. The numerical values of [k, k12, and k21]
which is estimated through the determination of the mathematical hybrid constants (A, B, a, b, T) also
predict the tissue concentration of the drug, biological half-life as well.
Some Mixed Quadrature Rules for Approximate Evaluation of Real Cauchy Princip...IJERD Editor
In this paper some mixed quadrature rules have been constructed for numerical integration of real
Cauchy principal value integrals and their asymptotic error estimates have been derived. The numerical
verification of the rules has been done by considering some standard Cauchy principal value integrals.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
Phase is a form of matter that is uniform with respect to chemical composition and the state of aggregation on both microscopic and macroscopic length scales.
Determination of Hess’s Law (Direct or Indirect)
Exact Solutions of Coupled Parallel Resonant Circuits Equations by Decomposit...AI Publications
In this paper, we provide the solution of a modeled parallel resonant circuit using the decomposition method. The parallel resonant circuit also known as resistor (R) in ohms, inductor (L) in Henry and capacitor (C) in farads (RLC) circuit is used in turning radio or audio receivers. The mathematical models are in a system of ordinary differential equations (ODE), which we solve using the Adomian Decomposition Method (ADM). We discovered that this method gave exact solutions as can be obtained using any traditionally known analytic method. These findings are illustrated in three test problems.
A Mathematical Review to Estimate the Fate of a Drug Following Open Two Compa...BRNSS Publication Hub
This paper deals with the application of Laplace Transform [L(f)(s) = F(s) = e-ts f(t)dt] to derive the
formula [(Cp
(t)= Ae-at+ Be-bt] and [Ct
(t)= Te-bt-Te-at] to estimate the fate of a drug in the mammillary body
with the prediction of the biological parameters [k, k12, and k21]. The numerical values of [k, k12, and k21]
which is estimated through the determination of the mathematical hybrid constants (A, B, a, b, T) also
predict the tissue concentration of the drug, biological half-life as well.
Some Mixed Quadrature Rules for Approximate Evaluation of Real Cauchy Princip...IJERD Editor
In this paper some mixed quadrature rules have been constructed for numerical integration of real
Cauchy principal value integrals and their asymptotic error estimates have been derived. The numerical
verification of the rules has been done by considering some standard Cauchy principal value integrals.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
Phase is a form of matter that is uniform with respect to chemical composition and the state of aggregation on both microscopic and macroscopic length scales.
Determination of Hess’s Law (Direct or Indirect)
Generally, summarize the methods you’ve learnt so far including this subject to solve systems of linear algebraic equations with their specifications. How numerical methods learnt here – the Jacobi’s and Gauss-Seidel's methods – are better than analytical methods under the specifications these can be used? Justify your answer with concrete reasons. Solve the following pipe-reactor system for unknown concentrations of solution inside the five reactors using Jacobi’s and Gauss-Seidel methods to not more than 5 iterations. Also plot maximum absolute percentage errors in all concentration's iterations-wise by the both methods to see demonstrate which method is better and why? Besides, also apply Gauss-Jordon method for the solution, and compare the computational complexities of the three methods.
Medical Conferences, Pharma Conferences, Engineering Conferences, Science Conferences, Manufacturing Conferences, Social Science Conferences, Business Conferences, Scientific Conferences Malaysia, Thailand, Singapore, Hong Kong, Dubai, Turkey 2014 2015 2016
Global Research & Development Services (GRDS) is a leading academic event organizer, publishing Open Access Journals and conducting several professionally organized international conferences all over the globe annually. GRDS aims to disseminate knowledge and innovation with the help of its International Conferences and open access publications. GRDS International conferences are world-class events which provide a meaningful platform for researchers, students, academicians, institutions, entrepreneurs, industries and practitioners to create, share and disseminate knowledge and innovation and to develop long-lasting network and collaboration.
GRDS is a blend of Open Access Publications and world-wide International Conferences and Academic events. The prime mission of GRDS is to make continuous efforts in transforming the lives of people around the world through education, application of research and innovative ideas.
Global Research & Development Services (GRDS) is also active in the field of Research Funding, Research Consultancy, Training and Workshops along with International Conferences and Open Access Publications.
International Conferences 2014 – 2015
Malaysia Conferences, Thailand Conferences, Singapore Conferences, Hong Kong Conferences, Dubai Conferences, Turkey Conferences, Conference Listing, Conference Alerts
Adomian Decomposition Method for Solving the Nonlinear Heat EquationIJERA Editor
This paper studies the application of the Adomian Decomposition Method to find the exact and approximate solutions of the heat equation with power nonlinearity. First, the relevant literature is studied in understanding the importance and extent of applicability of the method in the applied science. The literature review has been incorporated in the introduction of the paper. The rest of the paper is divided in three further sections. The first part Adomian Decomposition Method provides a step-by-step guide of applying the method on any heat equation with nonlinearity. The second section is labeled as Applications. It considers two examples from the previous works of Pumak (2005) and Hetmaniok et al. (2010) to find the exact and approximate solutions of the equations respectively.
Definition - Mechanism - Effect of dielectric constant on the rate of reactions in solutions - Salt effect - Primary salt effect - Bronsted – Bjerrum equation - Secondary salt effect - Effect of pressure on rate of reaction in solution - Volume of activation - Significance
วารสารวิชาการเทคโนโลยีพลังงานและสิ่งแวดล้อม
Journal of Energy and Environment Technology
ปีที่ 2 ฉบับที่ 1 เดือน มกราคม - มิถุนายน 2558
Vol. 1, No. 2, January – June [2015]
FORTRAN is used as a numerical and scientific computing language. The main objective of the lab work is to understand FORTRAN language using which we solve simple numerical problems and compare different methodologies. Through this project we make use of various functions of FORTRAN and solve a FDM simple heat equation problem applying different conditions viz. Dirichlet and Von Neumann. The given problems are solved analytically then built and compiled using a free integrated development environment called CODE::BLOCKS [1] which is an open source platform for FORTRAN and C.
Generally, summarize the methods you’ve learnt so far including this subject to solve systems of linear algebraic equations with their specifications. How numerical methods learnt here – the Jacobi’s and Gauss-Seidel's methods – are better than analytical methods under the specifications these can be used? Justify your answer with concrete reasons. Solve the following pipe-reactor system for unknown concentrations of solution inside the five reactors using Jacobi’s and Gauss-Seidel methods to not more than 5 iterations. Also plot maximum absolute percentage errors in all concentration's iterations-wise by the both methods to see demonstrate which method is better and why? Besides, also apply Gauss-Jordon method for the solution, and compare the computational complexities of the three methods.
Medical Conferences, Pharma Conferences, Engineering Conferences, Science Conferences, Manufacturing Conferences, Social Science Conferences, Business Conferences, Scientific Conferences Malaysia, Thailand, Singapore, Hong Kong, Dubai, Turkey 2014 2015 2016
Global Research & Development Services (GRDS) is a leading academic event organizer, publishing Open Access Journals and conducting several professionally organized international conferences all over the globe annually. GRDS aims to disseminate knowledge and innovation with the help of its International Conferences and open access publications. GRDS International conferences are world-class events which provide a meaningful platform for researchers, students, academicians, institutions, entrepreneurs, industries and practitioners to create, share and disseminate knowledge and innovation and to develop long-lasting network and collaboration.
GRDS is a blend of Open Access Publications and world-wide International Conferences and Academic events. The prime mission of GRDS is to make continuous efforts in transforming the lives of people around the world through education, application of research and innovative ideas.
Global Research & Development Services (GRDS) is also active in the field of Research Funding, Research Consultancy, Training and Workshops along with International Conferences and Open Access Publications.
International Conferences 2014 – 2015
Malaysia Conferences, Thailand Conferences, Singapore Conferences, Hong Kong Conferences, Dubai Conferences, Turkey Conferences, Conference Listing, Conference Alerts
Adomian Decomposition Method for Solving the Nonlinear Heat EquationIJERA Editor
This paper studies the application of the Adomian Decomposition Method to find the exact and approximate solutions of the heat equation with power nonlinearity. First, the relevant literature is studied in understanding the importance and extent of applicability of the method in the applied science. The literature review has been incorporated in the introduction of the paper. The rest of the paper is divided in three further sections. The first part Adomian Decomposition Method provides a step-by-step guide of applying the method on any heat equation with nonlinearity. The second section is labeled as Applications. It considers two examples from the previous works of Pumak (2005) and Hetmaniok et al. (2010) to find the exact and approximate solutions of the equations respectively.
Definition - Mechanism - Effect of dielectric constant on the rate of reactions in solutions - Salt effect - Primary salt effect - Bronsted – Bjerrum equation - Secondary salt effect - Effect of pressure on rate of reaction in solution - Volume of activation - Significance
วารสารวิชาการเทคโนโลยีพลังงานและสิ่งแวดล้อม
Journal of Energy and Environment Technology
ปีที่ 2 ฉบับที่ 1 เดือน มกราคม - มิถุนายน 2558
Vol. 1, No. 2, January – June [2015]
FORTRAN is used as a numerical and scientific computing language. The main objective of the lab work is to understand FORTRAN language using which we solve simple numerical problems and compare different methodologies. Through this project we make use of various functions of FORTRAN and solve a FDM simple heat equation problem applying different conditions viz. Dirichlet and Von Neumann. The given problems are solved analytically then built and compiled using a free integrated development environment called CODE::BLOCKS [1] which is an open source platform for FORTRAN and C.
A solution of the Burger’s equation arising in the Longitudinal Dispersion Ph...IOSR Journals
The goal of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. The solution of the Burger’s equation for the dispersion problem is
presented by approach to Sumudu transformation. The solution is obtained by using suitable conditions and is
more simplified under the standard assumptions.
Regional gradient optimal control problem governed by a distributed bilinear ...TELKOMNIKA JOURNAL
This paper gives an extension of previous work on gradient optimal control of distributed parabolic systems to the case of distributed bilinear systems which are a type of nonlinear systems. We introduce the notion of flux optimal control of distributed bilinear systems. The idea is trying to achieve a neighborhood of the gradient state of the considered system by minimizing a nonlinear quadratic cost. Using optimization techniques, a method showing how to reach a desired flux at a final time, only on internal subregion of the system domain will be proposed. The proposed simulation illustrates the theoretical approach by commanding the heat bilinear equation flux to a desired profile.
Analytical solutions of linear and non-linear incommensurate fractional-order...nooriasukmaningtyas
In this paper, a new analytical method is developed for solving linear and
non-linear fractional-order coupled systems of incommensurate orders. The
system consists of two fractional-order differential equations of orders
. The proposed approach is performed by decoupling the system
into two fractional-order differential equations; the first one is a fractionalorder differential equation (FoDE) of one variable of order , while the
second one depends on the solution of the first one. The general solution of
the coupled system is obtained using the adomian decomposition method
(ADM). The main ideas of this work are verified via several examples of
linear and nonlinear systems, and the numerical simulations are performed
using mathematica.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
New Two-Step Method with Fifth-Order Convergence for Solving Nonlinear Equationsinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
Applications of Homotopy perturbation Method and Sumudu Transform for Solving...IJRES Journal
In this paper, we make use of the properties of the Sumudu transform to find the exact solution of
fractional initial-boundary value problem (FIBVP) and fractional KDV equation. The method, namely,
homotopy perturbation Sumudu transform method, is the combination of the Sumudu transform and the
HPM using He’s polynomials. This method is very powerful and professional techniques for solving different
kinds of linear and nonlinear fractional differential equations arising in different fields of science and
engineering. We also present two different examples to illustrate the preciseness and effectiveness of this
method.
An optimal design of current conveyors using a hybrid-based metaheuristic alg...IJECEIAES
This paper focuses on the optimal sizing of a positive second-generation current conveyor (CCII+), employing a hybrid algorithm named DE-ACO, which is derived from the combination of differential evolution (DE) and ant colony optimization (ACO) algorithms. The basic idea of this hybridization is to apply the DE algorithm for the ACO algorithm’s initialization stage. Benchmark test functions were used to evaluate the proposed algorithm’s performance regarding the quality of the optimal solution, robustness, and computation time. Furthermore, the DE-ACO has been applied to optimize the CCII+ performances. SPICE simulation is utilized to validate the achieved results, and a comparison with the standard DE and ACO algorithms is reported. The results highlight that DE-ACO outperforms both ACO and DE.
SUCCESSIVE LINEARIZATION SOLUTION OF A BOUNDARY LAYER CONVECTIVE HEAT TRANSFE...ijcsa
The purpose of this paper is to discuss the flow of forced convection over a flat plate. The governing partial
differential equations are transformed into ordinary differential equations using suitable transformations.
The resulting equations were solved using a recent semi-numerical scheme known as the successive
linearization method (SLM). A comparison between the obtained results with homotopy perturbation method and numerical method (NM) has been included to test the accuracy and convergence of the method.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
Stochastic Analysis of Van der Pol OscillatorModel Using Wiener HermiteExpans...IJERA Editor
We study a model related to Van der Poloscillatorunder an external stochastic excitation described by white
noise process. This study is limited to find the Gaussian behavior of the stochastic solution processes related to
the model. Under the application ofWiener-Hermite expansion, a deterministic system is generated to describe
the Gaussian solution parameters (Mean and Variance).The deterministic system solution is approximated by
applying the multi-stepdifferential transformedmethodand the results are compared with NDSolveMathematica
10 package. Some case studies are considered to illustrate some comparisons for the obtained results related to
the Gaussian behavior parameters.
Stochastic Analysis of Van der Pol OscillatorModel Using Wiener HermiteExpans...IJERA Editor
We study a model related to Van der Poloscillatorunder an external stochastic excitation described by white
noise process. This study is limited to find the Gaussian behavior of the stochastic solution processes related to
the model. Under the application ofWiener-Hermite expansion, a deterministic system is generated to describe
the Gaussian solution parameters (Mean and Variance).The deterministic system solution is approximated by
applying the multi-stepdifferential transformedmethodand the results are compared with NDSolveMathematica
10 package. Some case studies are considered to illustrate some comparisons for the obtained results related to
the Gaussian behavior parameters.
Similar to The variational iteration method for calculating carbon dioxide absorbed into phenyl glycidyl ether (20)
An Examination of Effectuation Dimension as Financing Practice of Small and M...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Does Goods and Services Tax (GST) Leads to Indian Economic Development?iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Childhood Factors that influence success in later lifeiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Emotional Intelligence and Work Performance Relationship: A Study on Sales Pe...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Customer’s Acceptance of Internet Banking in Dubaiiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
A Study of Employee Satisfaction relating to Job Security & Working Hours amo...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Consumer Perspectives on Brand Preference: A Choice Based Model Approachiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Student`S Approach towards Social Network Sitesiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Broadcast Management in Nigeria: The systems approach as an imperativeiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
A Study on Retailer’s Perception on Soya Products with Special Reference to T...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
A Study Factors Influence on Organisation Citizenship Behaviour in Corporate ...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Consumers’ Behaviour on Sony Xperia: A Case Study on Bangladeshiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Design of a Balanced Scorecard on Nonprofit Organizations (Study on Yayasan P...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Public Sector Reforms and Outsourcing Services in Nigeria: An Empirical Evalu...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Media Innovations and its Impact on Brand awareness & Considerationiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Customer experience in supermarkets and hypermarkets – A comparative studyiosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Social Media and Small Businesses: A Combinational Strategic Approach under t...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Secretarial Performance and the Gender Question (A Study of Selected Tertiary...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Implementation of Quality Management principles at Zimbabwe Open University (...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Organizational Conflicts Management In Selected Organizaions In Lagos State, ...iosrjce
IOSR Journal of Business and Management (IOSR-JBM) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of business and managemant and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications inbusiness and management. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
Phenomics assisted breeding in crop improvementIshaGoswami9
As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
change, and increasing global population, crop yield and quality need to be improved in a sustainable way over the coming decades. Genetic improvement by breeding is the best way to increase crop productivity. With the rapid progression of functional
genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
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The variational iteration method for calculating carbon dioxide absorbed into phenyl glycidyl ether
1. IOSR Journal of Mathematics (IOSR-JM)
e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 11, Issue 6 Ver. 1 (Nov. - Dec. 2015), PP 99-105
www.iosrjournals.org
DOI: 10.9790/5728-116199105 www.iosrjournals.org 99 | Page
The variational iteration method for calculating carbon dioxide
absorbed into phenyl glycidyl ether
M. A. AL-Jawary1
, G. H. Radhi2
1
(Head of Department of Mathematics, College of Education for Pure Science (Ibn AL-Haytham) / Baghdad
University, Iraq, Baghdad)
2
(Department of Mathematics, College of Education for Pure Science (Ibn AL-Haytham) / Baghdad University,
Iraq, Baghdad)
Abstract: In this paper, the variational iteration method (VIM) is used to get an approximate solution for a
system of two coupled nonlinear ordinary differential equations which represent the concentrations of carbon
dioxide 𝐶𝑂2 and phenyl glycidyl ether. In this system there are boundary conditions of Dirichlet type and the
other is a mixed set of Neumann and Dirichlet type. Our calculations evidenced by tables and figures for the
analysis of the maximal error remainder values. The variational iteration method gives approximate solutions
with fast convergence. Comparison with the results obtained by the Adomian decomposition method (ADM)
reveals that the numerical solutions obtained by the VIM converge faster than those of Adomian's method. The
software we used in our study of these calculations is Mathematica®
9.
Keywords - Variational iteration method, Lagrange multiplier, Carbon dioxide, Phenyl glycidyl ether.
I. Introduction
Among the very important gases in nature is carbon dioxide CO2 [1] where this gas is made up of only
one carbon atom with two atoms of oxygen [2]. Carbon dioxide is considered an important factor in plant
photosynthesis, in the powering of the pneumatic systems in robots used in extinguishing fires, carbonated soft
drinks industry and remove the caffeine from coffee,... etc. [2,3,4]. Carbon dioxide considered a rich and cheap
source of carbon. Benefits from carbon dioxide are considered an important development through the industry
of most useful materials and the reduction of the threat posed by greenhouse effect.
The chemical absorption of carbon dioxide into phenyl glycidyl ether solution containing a catalyst
THA-CP-MS41 in heterogeneous systems has been investigated by Park et al. [4] and Choe et al. [5].
Approximate analytical expression for the simple steady-state concentrations of CO2 and PGE using the
Adomian decomposition method is presented in [2]. However, the ADM required calculating the Adomian
polynomials which needs more time and calculations.
In 1999, the Variational Iteration Method was first suggested by the Chinese mathematician Ji-Haun
He [6, 7]. It can be applied to many differential and integral equations, linear and nonlinear, note that the finding
of the exact solution for many of nonlinear problems is not easy task. In comparison to other methods used for
solving the nonlinear differential equations [8], for example, Lie group method [9], homogeneous balance
method [10], inverse scattering method [11], Adomian's decomposition method [12,13,14] and He's homotopy
perturbation method (HPM) [15,16,17], the VIM is very effective, simple and does not require any restrictive
assumptions for nonlinear terms.
The VIM has an advantage make us adopt in to calculate this system of nonlinear ordinary differential
equations that is the VIM reduces the amount of calculations with survival maintain the higher accuracy in the
solution.
He's VIM provides the approximations by using the correction functional requiring the Lagrange's
multiplayer, while the ADM gives us components that are collected together to reach the solution and each
component takes a long time to calculate it because of the terms of Adomian's polynomial which represent the
nonlinear terms for both equations in the system [12,13]. The VIM does not need to calculate small parameters
like as in the traditional perturbation methods, therefore the limitations of these methods has been eliminated. It
is worth mentioning that this method is a modification for the general Lagrange multiplier method [18].
In this work, the VIM will be implemented to get an approximate solution for a system of two coupled
nonlinear ordinary differential equations which represent the concentrations of carbon dioxide CO2 and phenyl
glycidyl ether.
This paper has been organized as follows. The steady-state concentrations of carbon dioxide absorbed
into phenyl glycidyl ether solutions is given in details in section II. The variational iteration method is presented
in section III. In section IV, solving the system of steady-state concentrations of CO2 and PGE by the VIM will
be given. Section V provides numerical simulation and the conclusion will be followed in section VI.
2. The variational iteration method for calculating carbon dioxide absorbed into phenyl glycidyl
DOI: 10.9790/5728-116199105 www.iosrjournals.org 100 | Page
II. Steady-State Concentrations of Carbon Dioxide Absorbed into Phenyl Glycidyl Ether
A system of two nonlinear differential equations represents the steady-state concentrations of two
chemicals; carbon dioxide CO2 and PGE is given in [2]. This system can be represented by [19]:
𝑢´´ 𝑥 =
𝛼1 𝑢 𝑥 𝑣(𝑥)
1 + 𝛽1 𝑢 𝑥 + 𝛽2 𝑣(𝑥)
, (1)
𝑣´´ 𝑥 =
𝛼2 𝑢 𝑥 𝑣 𝑥
1 + 𝛽1 𝑢 𝑥 +𝛽2 𝑣 𝑥
, (2)
with the boundary conditions
𝑢 0 = 1, 𝑣′ 0 = 0,
𝑢 1 = 𝑘, 𝑣 1 = 1.
Where, 𝑢 𝑥 is the concentration of CO2, 𝑣 𝑥 is the concentration of PGE, 𝛼1, 𝛼2, 𝛽1 and 𝛽2 are the parameters
of normalized system, 𝑥 is the "dimensionless distance" from the center and 𝑘 is the concentration of CO2 at the
surface catalyst [2].
This system of equations has been solved by the Adomian decomposition method [2,19] where it was
calculated acceptable approximate results with the statement of the maximal error remainder and the amount of
the accuracy [19], after converted into system of two coupled integral equations and take the advantage of the
given boundary conditions with this problem. However, due to the nonlinear terms, the Adomian polynomials
are calculated which required more calculations and time.
In this work, we will solve this nonlinear system of these two coupled nonlinear ordinary differential
equations [2,19] in a straightforward manner by using the Variational Iteration Method (VIM), details of the
VIM can be found in [20-25].
Equations (1) and 2 can be written as:
𝑢´´ 𝑥 1 + 𝛽1 𝑢 𝑥 + 𝛽2 𝑣 𝑥 = 𝛼1 𝑢 𝑥 𝑣 𝑥 , (3)
𝑣´´ 𝑥 1 + 𝛽1 𝑢 𝑥 + 𝛽2 𝑣 𝑥 = 𝛼2 𝑢 𝑥 𝑣 𝑥 . (4)
The Eqs. (3),(4) will be solved by using the VIM.
III. The Variational Iteration Method:
According to the VIM [20-25], consider the following differential equation:
𝐿𝑢 + 𝑁𝑢 = 𝑔 𝑥 , (5)
where L is the linear operator, 𝑁 is the nonlinear operator and 𝑔 𝑥 is the inhomogeneous term. The
method employs the correction functional as follows:
𝑢 𝑛+1 𝑥 = 𝑢 𝑛 𝑥 + 𝜆(𝐿𝑢 𝑛 𝑡 + 𝑁𝑢 𝑛 𝑡 − 𝑔 𝑡 )
𝑥
0
𝑑𝑡, (6)
where 𝜆 is the Lagrange multiplier [23, 24], which can be identified optimally via the variational theory [24], the
subscript 𝑛 represents the rank of the approximation 𝑢 𝑛 and 𝑢 𝑛 is the restricted variation that is 𝛿𝑢 𝑛 = 0. It is
obvious now that the main steps of the He’s variational iteration method require first the determination of the
Lagrange multiplier 𝜆 t that will be identified optimally. Integration by parts is usually used for the selection of
the Lagrange multiplier 𝜆 t . In other words we can use
∫𝜆 𝑡 𝑢´ 𝑛 𝑡 𝑑𝑡 = 𝜆 𝑡 𝑢 𝑛 𝑡 − ∫𝜆´ 𝑡 𝑢 𝑛 𝑡 𝑑𝑡,
∫𝜆 𝑡 𝑢´´ 𝑛 𝑡 𝑑𝑡 = 𝜆 𝑡 𝑢´ 𝑛 𝑡 − 𝜆´ 𝑡 𝑢 𝑛 𝑡 + ∫𝜆´´ 𝑡 𝑢 𝑛 𝑡 𝑑𝑡, (7)
and so on. Having determined the Lagrange multiplier 𝜆(𝑡), the successive approximations 𝑢 𝑛+1, 𝑛 ≥ 0, of the
solution 𝑢 will be immediately obtained upon using any selective function 𝑢0.
In general the exact solution can be obtained by
𝑢(𝑥) = lim
𝑛→∞
𝑢 𝑛 𝑥 . (8)
This method gives rapidly convergent successive approximations of the exact solution if such a
solution exists, otherwise a few approximations can be used for numerical purposes. The VIM does not require
restrictive conditions or specific assumptions as we have seen in other methods of other studies pertaining to the
differential equations such as perturbation techniques.
3. The variational iteration method for calculating carbon dioxide absorbed into phenyl glycidyl
DOI: 10.9790/5728-116199105 www.iosrjournals.org 101 | Page
IV. Solving the system of steady-state concentrations of CO2 and PGE by the VIM:
Let us rewrite Eqs (3) and (4) as:
𝑢´´ 𝑥 1 + 𝛽1 𝑢 𝑥 + 𝛽2 𝑣 𝑥 − 𝛼1 𝑢 𝑥 𝑣 𝑥 = 0, (9)
𝑣´´ 𝑥 1 + 𝛽1 𝑢 𝑥 + 𝛽2 𝑣 𝑥 − 𝛼2 𝑢 𝑥 𝑣 𝑥 = 0, (10)
with the boundary conditions
𝑢 0 = 1, 𝑣′ 0 = 0,
𝑢 1 = 𝑘, 𝑣 1 = 1.
The correction functional for this system is given as
𝑢 𝑛 𝑥 = 𝑢 𝑛+1(𝑥) + 𝜆1 𝑡 (𝑢´´ 𝑛(𝑡)(1 + 𝛽1 𝑢 𝑛 𝑡 + 𝛽2 𝑣 𝑛 𝑡 ) − 𝛼1 𝑢 𝑛 𝑡 𝑣𝑛 𝑡
𝑥
0
)𝑑𝑡, (11)
𝑣 𝑛 𝑥 = 𝑣 𝑛+1(𝑥) + 𝜆1 𝑡 (𝑣´´ 𝑛(𝑡)(1 + 𝛽1 𝑢 𝑛 𝑡 + 𝛽2 𝑣 𝑛 𝑡 ) − 𝛼2 𝑢 𝑛 𝑡 𝑣𝑛 𝑡
𝑥
0
)𝑑𝑡, (12)
this yields the stationary conditions [27]
1 − 𝜆´1|𝑡=𝑥 = 0, 𝜆1|𝑡=𝑥 = 0, 𝜆´´1|𝑡=𝑥 = 0, (13)
1 − 𝜆´2|𝑡=𝑥 = 0, 𝜆2|𝑡=𝑥 = 0, 𝜆´´2|𝑡=𝑥 = 0.
As a result, those will be obtained
𝜆1 𝑡 = 𝜆2 𝑡 = 𝑡 − 𝑥, (14)
substitute Eq. (14) into Eqs. (11) and (12), gives the iterations formulas:
𝑢 𝑛 𝑥 = 𝑢 𝑛+1 𝑥 + (𝑡 − 𝑥)(𝑢´´ 𝑛 (𝑡)(1 + 𝛽1 𝑢 𝑛 𝑡 + 𝛽2 𝑣 𝑛 𝑡 ) − 𝛼1 𝑢 𝑛 𝑡 𝑣 𝑛 𝑡
𝑥
0
)𝑑𝑡, (15)
𝑣 𝑛 𝑥 = 𝑣 𝑛+1 𝑥 + (𝑡 − 𝑥)(𝑣´´ 𝑛(𝑡)(1 + 𝛽1 𝑢 𝑛 𝑡 + 𝛽2 𝑣 𝑛 𝑡 ) − 𝛼2 𝑢 𝑛 𝑡 𝑣 𝑛 𝑡
𝑥
0
)𝑑𝑡, 𝑛 ≥ 0, (16)
the initial approximations have been taken: 𝑢0 𝑥 = 𝑥 𝑚
and 𝑣0 𝑥 = 𝑥 𝑚
, with 𝑚 = 1.
The following approximations are achieved:
𝑢0 𝑥 = 𝑥,
𝑣0 𝑥 = 𝑥,
𝑢1 𝑥 = 𝑥 + (𝑡 − 𝑥)(𝑢´´0(𝑡)(1 + 𝛽1 𝑢0 𝑡 + 𝛽2 𝑣0 𝑡 ) − 𝛼1 𝑢0 𝑡 𝑣0 𝑡
𝑥
0
)𝑑𝑡
= 𝑥 +
𝑥4
α1
12
,
𝑣1 𝑥 = 𝑥 + (𝑡 − 𝑥)(𝑣´´0(𝑡)(1 + 𝛽1 𝑢0 𝑡 + 𝛽2 𝑣0 𝑡 ) − 𝛼2 𝑢0 𝑡 𝑣0 𝑡
𝑥
0
)𝑑𝑡
= 𝑥 +
𝑥4
α2
12
,
𝑢2 𝑥 = 𝑥 +
𝑥4
α1
12
+ (𝑡 − 𝑥)(𝑢´´1(𝑡)(1 + 𝛽1 𝑢1 𝑡 + 𝛽2 𝑣1 𝑡 ) − 𝛼1 𝑢1 𝑡 𝑣1 𝑡
𝑥
0
)𝑑𝑡
= 𝑥 +
𝑥4
𝛼1
12
+
𝑥5
𝛼1(7𝑥5
𝛼1α2 + 180𝑥2
(𝛼1 + α2) − 4536(𝛽1 + 𝛽2) − 135𝑥3
(𝛼1 𝛽1 + α2 𝛽2))
90720
,
𝑣2 𝑥 = 𝑥 +
𝑥4
α2
12
+ (𝑡 − 𝑥)(𝑣´´1(𝑡)(1 + 𝛽1 𝑢1 𝑡 + 𝛽2 𝑣1 𝑡 ) − 𝛼2 𝑢1 𝑡 𝑣1 𝑡
𝑥
0
)𝑑𝑡
= 𝑥 +
𝑥4
𝛼1
12
+
𝑥5
𝛼1(7𝑥5
𝛼1α2 + 180𝑥2
(𝛼1 + α2) − 4536(𝛽1 + 𝛽2) − 135𝑥3
(𝛼1 𝛽1 + α2 𝛽2))
90720
.
(17)
Thus we continue to obtain successive approximations of 𝑢 𝑛 𝑥 and 𝑣 𝑛 𝑥 but for brevity not listed. The
calculations are obtained by using Mathematica 9.
In order to examine the accuracy of the achieved approximate solution, the convenience functions of the error
remainder will be [19]:
𝐸𝑅1,𝑛 𝑥 = 𝑢´´ 𝑛 𝑡 1 + 𝛽1 𝑢 𝑛 𝑡 + 𝛽2 𝑣 𝑛 𝑡 − 𝛼1 𝑢 𝑛 𝑡 𝑣 𝑛 𝑡 , (18)
𝐸𝑅2,𝑛 𝑥 = 𝑣´´ 𝑛 𝑡 1 + 𝛽1 𝑢 𝑛 𝑡 + 𝛽2 𝑣 𝑛 𝑡 − 𝛼2 𝑢 𝑛 𝑡 𝑣 𝑛 𝑡 , (19)
and the maximal error remainder parameters are
𝑀𝐸𝑅1,𝑛 = max
0≤𝑥≤1
𝐸𝑅1,𝑛 𝑥 , 𝑀𝐸𝑅2,𝑛 = max
0≤𝑥≤1
𝐸𝑅2,𝑛 𝑥 . (20)
4. The variational iteration method for calculating carbon dioxide absorbed into phenyl glycidyl
DOI: 10.9790/5728-116199105 www.iosrjournals.org 102 | Page
V. Numerical simulations:
The values of the parameters have been chosen: 𝛼1 = 1, 𝛼2 = 2, 𝛽1 = 1, 𝛽2 = 3 and 𝑘 = 0.5 as in
[19], then we calculate the error remainder with the maximal error remainder parameters and the approximate
solutions. Below we have created both 𝑀𝐸𝑅1,𝑛 and 𝑀𝐸𝑅2,𝑛 as the values of n increase from 1 to 4 and in
comparison with the Adomian decomposition method [19,12]. It can be seen that the maximal error remainder
values of the VIM is the least of those obtained from the ADM. Therefore, better accuracy achieved for both
𝑀𝐸𝑅1,𝑛 and 𝑀𝐸𝑅2,𝑛 :
Table.1: Comparison between the ADM and the VIM of 𝑴𝑬𝑹 𝟏,𝒏
Table.2: Comparison between the ADM and the VIM of 𝑴𝑬𝑹 𝟐,𝒏
We insert below the Figs. 1 and 2, respectively, that show the analysis of the maximal error remainders
for both 𝑀𝐸𝑅1,𝑛 and 𝑀𝐸𝑅2,𝑛, where the points are lay on a straight lines which mean we achieved exponential
rate of convergence.
Fig.1: Logarithmic plots of 𝑀𝐸𝑅1,𝑛 versus n is 1 through 4 and m=1
𝑛 𝑀𝐸𝑅1,𝑛 by the
ADM[19]
𝑀𝐸𝑅1,𝑛 by the
VIM
1 0.2 0.003
2 0.0888889 0.00159895
3 0.00888889 0.00063952
4 0.00099943 0.0002558
𝑛 𝑀𝐸𝑅2,𝑛 by the
ADM[19]
𝑀𝐸𝑅2,𝑛 by the
VIM
1 0.4 0.00799617
2 0.177778 0.0031979
3 0.0177778 0.00127904
4 0.00099943 0.000511601
5. The variational iteration method for calculating carbon dioxide absorbed into phenyl glycidyl
DOI: 10.9790/5728-116199105 www.iosrjournals.org 103 | Page
Fig.2: Logarithmic plots of 𝑀𝐸𝑅2,𝑛 versus n is 1 through 4 and m=1
It is interesting to point out here, by increasing the power of the values of 𝑥 (initial approximations) for
both 𝑢 𝑛 𝑥 and 𝑣 𝑛 𝑥 , the error decreases and the accuracy will be higher. Moreover, it can be seen clearly from
tables 1, 2, Figs 1 and 2 that by increasing the iterations (n from 1 to 4) we achieved good accuracy as well.
Fig.3: Logarithmic plots of 𝑀𝐸𝑅1,𝑛 versus n is 1 through 4 and m=30
Fig.4: Logarithmic plots of 𝑀𝐸𝑅2,𝑛 versus n is 1 through 4 and m=30
6. The variational iteration method for calculating carbon dioxide absorbed into phenyl glycidyl
DOI: 10.9790/5728-116199105 www.iosrjournals.org 104 | Page
Tables 3 and 4 show the maximal error remainders are decreases when the power of 𝒙 is increases for
both 𝒖 𝒏(𝒙) and 𝒗 𝒏(𝒙) :
Table.3: the maximal error remainder: 𝑀𝐸𝑅1,𝑛 by the VIM Where n=1,…,4 and the power of 𝑥 is 𝑚
Table.4: the maximal error remainder: 𝑀𝐸𝑅2,𝑛 by the VIM Where n=1,…,4 and the power of 𝑥 is 𝑚
VI. Conclusion
In this paper, He's variational iteration method has been successfully applied to calculate the
concentrations of carbon dioxide absorbed into phenyl glycidyl ether. The VIM provides the solutions in the
form of convergent series with easily computed components. Unlike the ADM where computational algorithms
required to calculate the Adomian polynomials to handle the nonlinear terms. Comparison with Adomian's
decomposition method reveals that the numerical solutions obtained by the VIM converge faster than those of
Adomian's method. It has been achieved that from figures and tables that the maximal error remainders
decreased when the number of iterations are increased. Moreover, as the power of x (initial approximation) is
increased the maximal error remainders decreased.
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