In this paper, an implicit one-step method for numerical solution of second order Initial Value
Problems of Ordinary Differential Equations has been developed by collocation and interpolation technique.
The one-step method was developed using Chebyshev polynomial as basis function and, the method was
augmented by the introduction of offstep points in order to bring about zero stability and upgrade the order of
consistency of the new method. An advantage of the derived continuous scheme is that it can produce several
outputs of solution at the off-grid points without requiring additional interpolation. Numerical examples are
presented to portray the applicability and the efficiency of the method.
Block Hybrid Method for the Solution of General Second Order Ordinary Differe...QUESTJOURNAL
ABSTRACT: We consider the construction of block hybrid method for the solution of general second order ODEs. Derivation of the method was based on the use of hermite polynomial as basis function. The main method and its additional equations are obtained from the same continuous formulation via interpolation and collocation procedures. The method is then applied in block form as simultaneous numerical integrator, this approach eliminates requirement for starting values, and it also reduces computational effort. The stability properties of the method is discussed and the stability region shown. Two numerical experiments were given to illustrate the accuracy and efficiency of the new method.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Fourth order improved finite difference approach to pure bending analysis o...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Block Hybrid Method for the Solution of General Second Order Ordinary Differe...QUESTJOURNAL
ABSTRACT: We consider the construction of block hybrid method for the solution of general second order ODEs. Derivation of the method was based on the use of hermite polynomial as basis function. The main method and its additional equations are obtained from the same continuous formulation via interpolation and collocation procedures. The method is then applied in block form as simultaneous numerical integrator, this approach eliminates requirement for starting values, and it also reduces computational effort. The stability properties of the method is discussed and the stability region shown. Two numerical experiments were given to illustrate the accuracy and efficiency of the new method.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Fourth order improved finite difference approach to pure bending analysis o...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
RESIDUALS AND INFLUENCE IN NONLINEAR REGRESSION FOR REPEATED MEASUREMENT DATAorajjournal
All observations don’t have equal significance in regression analysis. Diagnostics of observations is an important aspect of model building. In this paper, we use diagnostics method to detect residuals and influential points in nonlinear regression for repeated measurement data. Cook distance and Gauss newton method have been proposed to identify the outliers in nonlinear regression analysis and parameter estimation. Most of these techniques based on graphical representations of residuals, hat matrix and case deletion measures. The results
show us detection of single and multiple outliers cases in repeated measurement data. We use these techniques
to explore performance of residuals and influence in nonlinear regression model.
Accurate Numerical Method for Singular Initial-Value Problemsaciijournal
In this paper, an accurate numerical method is presented to find the numerical solution of the singular initial value problems. The second-order singular initial value problem under consideration is transferred into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods is confirmed by solving three model examples, and the obtained approximate solutions are compared with the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical method for solving the singular initial value problems.
Numerical Solution to Ninth order Non- Linear Differential Equation Using the...rahulmonikasharma
In this paper, Collocation method using recursive form of Ninth degree B-spline functions as basis is developed and employed to find the numerical solution for ninth order boundary value problems. Non linear boundary value problem is considered to test the performance, stability and accuracy of the present developed method.
A ( )-Stable Order Ten Second Derivative Block Multistep Method for Stiff I...inventionjournals
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
Comparison of TCP congestion control mechanisms Tahoe, Newreno and VegasIOSR Journals
The widely used reliable transport protocol TCP, is an end to end protocol designed for the wireline
networks characterized by negligible random packet losses. This paper represents exploratory study of TCP
congestion control principles and mechanisms. Modern implementations of TCP contain four intertwined
algorithms: slow start, congestion avoidance, fast retransmit, and fast recovery. In addition to the standard
algorithms used in common implementations of TCP, this paper also describes some of the more common
proposals developed by researchers over the years. We also study, through extensive simulations, the
performance characteristics of four representative TCP schemes, namely TCP Tahoe, New Reno and Vegas
under the network conditions of bottleneck link capacities for wired network
Fault Detection Technique for Compact AES DesignIOSR Journals
Abstract: Cryptography is a method that has been developed to ensure the secrecy of messages and transfer data securely. Advanced Encryption Standard (AES) has been made as the first choice for many critical applications because of the high level of security and the fast hardware and software implementations, many of which are power and resource constrained and requires reliable and efficient hardware implementations. Naturally occurring and maliciously injected faults reduce the reliability of Advanced Encryption Standard (AES) and may leak confidential information. In this paper, a lightweight concurrent fault detection scheme for the AES is presented. In the proposed approach, the composite field S-box and inverse S-box are divided into blocks and the predicted parities of these blocks are obtained. For high speed applications, S-box implementation based on lookup tables is avoided. Instead, logic gate implementations based on composite fields are utilized. A compact architecture for the AES Mix-columns operation and its inverse is also presented. This parity-based fault detection scheme reaches the maximum fault coverage when compared to other methods of fault detection. The proposed fault detection technique for AES encryption and decryption has the least area and power consumption compared to their counterparts with similar fault detection capabilities. Index terms: AES, composite fields, parity prediction, fault detection, S-box.
Zooplanktonic Diversity and Trophic Status of Pashupatinath Pond in Relation ...IOSR Journals
Present investigation were carried out to physico chemical characterstics and trophic status of
Pashupatinath pond Mandsour (M.P.).water sample were collected seasonal basis for a period of December
2008 to September 2010 using plastic container .standard procedure were followed during collection
,preservation and analysis of water sample for various physicochemical and biological parameter .
The water quality is remained moderately alkaline PH (8.11) while electrical conductivity (0.2176 ms/cm), TDS
(187ppm) chloride (22.123ppm), Hardness(139.166ppm) and alkalinity (75.33ppm) show low mean value
.Average dissolve oxygen levels were at (7.771 ppm) ,while average nitrate and phosphate The water remained
modertly alkaline PH (7.95) while electrical conductance (0.2165ms/cm),TDS (153.66ppm)chloride (22.83ppm)
hardness (138.66ppm )and alkalinity (62.166 ppm) showed low mean values .Average dissolved oxygen level
were at (7.58 ppm ) while average nitrate and phosphate level were (0.2126ppm) and (0.5868 ppm) respectely
.On the basis of water quality parameter .Mirzapur dam was found to be oligotrophic. A low density of
Zooplankton were also observed during the study period
Synthesis, Characterization and Antibacterial Activity of New Complexes of So...IOSR Journals
Complexes of some lanthanide picrates (Ln3+ = Pr3+, Nd3+ and Dy3+) with benzo-18-crown-6 and 221-cryptand were synthesized and characterized by elemental analysis, FTIR, and UV-Visible. Spectrophotometric methods, thermal analysis (TGA & DTG), melting point, magnetic susceptibility and molar conductance. Also an in-vitro study on gram positive (Staphylococcus aureus) and gram negative bacteria (Escherichia coli, Salmonella and pseudomonas aeruginosa) was performed and the results were compared to those of the broad spectrum antibiotic Chloramphinicol. The benzo-18-crown-6 complexes have the general formula of [Ln.L.(Pic)2]Pic.nH2O , where; (Ln3+ = Pr3+, Nd3+, and Dy3+) , (L = Benzo-18-crown-6) , (Pic = Picrate anion) , (n = 1-2). In these complexes two picrate anions are coordinated to the metal ion through the phenolic oxygen and oxygen of the ortho nitro group, thus, the metal ions in these complexes have a coordination number of (10). The complexes of 221-cryptand have the general formula of [Ln.L.(Pic)]Pic2.nH2O where; (Ln3+ = Pr3+, Nd3+, and Dy3+), (L = 221-cryptand), (Pic = Picrate anion), (n = 1,2 or 7). In these complexes one picrate anion is coordinated to the metal ion, also through the phenolic oxygen and the oxygen from the ortho nitro group, thus the metal ions in the cryptand complexes have a coordination number of (9).
RESIDUALS AND INFLUENCE IN NONLINEAR REGRESSION FOR REPEATED MEASUREMENT DATAorajjournal
All observations don’t have equal significance in regression analysis. Diagnostics of observations is an important aspect of model building. In this paper, we use diagnostics method to detect residuals and influential points in nonlinear regression for repeated measurement data. Cook distance and Gauss newton method have been proposed to identify the outliers in nonlinear regression analysis and parameter estimation. Most of these techniques based on graphical representations of residuals, hat matrix and case deletion measures. The results
show us detection of single and multiple outliers cases in repeated measurement data. We use these techniques
to explore performance of residuals and influence in nonlinear regression model.
Accurate Numerical Method for Singular Initial-Value Problemsaciijournal
In this paper, an accurate numerical method is presented to find the numerical solution of the singular initial value problems. The second-order singular initial value problem under consideration is transferred into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods is confirmed by solving three model examples, and the obtained approximate solutions are compared with the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical method for solving the singular initial value problems.
Numerical Solution to Ninth order Non- Linear Differential Equation Using the...rahulmonikasharma
In this paper, Collocation method using recursive form of Ninth degree B-spline functions as basis is developed and employed to find the numerical solution for ninth order boundary value problems. Non linear boundary value problem is considered to test the performance, stability and accuracy of the present developed method.
A ( )-Stable Order Ten Second Derivative Block Multistep Method for Stiff I...inventionjournals
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
Comparison of TCP congestion control mechanisms Tahoe, Newreno and VegasIOSR Journals
The widely used reliable transport protocol TCP, is an end to end protocol designed for the wireline
networks characterized by negligible random packet losses. This paper represents exploratory study of TCP
congestion control principles and mechanisms. Modern implementations of TCP contain four intertwined
algorithms: slow start, congestion avoidance, fast retransmit, and fast recovery. In addition to the standard
algorithms used in common implementations of TCP, this paper also describes some of the more common
proposals developed by researchers over the years. We also study, through extensive simulations, the
performance characteristics of four representative TCP schemes, namely TCP Tahoe, New Reno and Vegas
under the network conditions of bottleneck link capacities for wired network
Fault Detection Technique for Compact AES DesignIOSR Journals
Abstract: Cryptography is a method that has been developed to ensure the secrecy of messages and transfer data securely. Advanced Encryption Standard (AES) has been made as the first choice for many critical applications because of the high level of security and the fast hardware and software implementations, many of which are power and resource constrained and requires reliable and efficient hardware implementations. Naturally occurring and maliciously injected faults reduce the reliability of Advanced Encryption Standard (AES) and may leak confidential information. In this paper, a lightweight concurrent fault detection scheme for the AES is presented. In the proposed approach, the composite field S-box and inverse S-box are divided into blocks and the predicted parities of these blocks are obtained. For high speed applications, S-box implementation based on lookup tables is avoided. Instead, logic gate implementations based on composite fields are utilized. A compact architecture for the AES Mix-columns operation and its inverse is also presented. This parity-based fault detection scheme reaches the maximum fault coverage when compared to other methods of fault detection. The proposed fault detection technique for AES encryption and decryption has the least area and power consumption compared to their counterparts with similar fault detection capabilities. Index terms: AES, composite fields, parity prediction, fault detection, S-box.
Zooplanktonic Diversity and Trophic Status of Pashupatinath Pond in Relation ...IOSR Journals
Present investigation were carried out to physico chemical characterstics and trophic status of
Pashupatinath pond Mandsour (M.P.).water sample were collected seasonal basis for a period of December
2008 to September 2010 using plastic container .standard procedure were followed during collection
,preservation and analysis of water sample for various physicochemical and biological parameter .
The water quality is remained moderately alkaline PH (8.11) while electrical conductivity (0.2176 ms/cm), TDS
(187ppm) chloride (22.123ppm), Hardness(139.166ppm) and alkalinity (75.33ppm) show low mean value
.Average dissolve oxygen levels were at (7.771 ppm) ,while average nitrate and phosphate The water remained
modertly alkaline PH (7.95) while electrical conductance (0.2165ms/cm),TDS (153.66ppm)chloride (22.83ppm)
hardness (138.66ppm )and alkalinity (62.166 ppm) showed low mean values .Average dissolved oxygen level
were at (7.58 ppm ) while average nitrate and phosphate level were (0.2126ppm) and (0.5868 ppm) respectely
.On the basis of water quality parameter .Mirzapur dam was found to be oligotrophic. A low density of
Zooplankton were also observed during the study period
Synthesis, Characterization and Antibacterial Activity of New Complexes of So...IOSR Journals
Complexes of some lanthanide picrates (Ln3+ = Pr3+, Nd3+ and Dy3+) with benzo-18-crown-6 and 221-cryptand were synthesized and characterized by elemental analysis, FTIR, and UV-Visible. Spectrophotometric methods, thermal analysis (TGA & DTG), melting point, magnetic susceptibility and molar conductance. Also an in-vitro study on gram positive (Staphylococcus aureus) and gram negative bacteria (Escherichia coli, Salmonella and pseudomonas aeruginosa) was performed and the results were compared to those of the broad spectrum antibiotic Chloramphinicol. The benzo-18-crown-6 complexes have the general formula of [Ln.L.(Pic)2]Pic.nH2O , where; (Ln3+ = Pr3+, Nd3+, and Dy3+) , (L = Benzo-18-crown-6) , (Pic = Picrate anion) , (n = 1-2). In these complexes two picrate anions are coordinated to the metal ion through the phenolic oxygen and oxygen of the ortho nitro group, thus, the metal ions in these complexes have a coordination number of (10). The complexes of 221-cryptand have the general formula of [Ln.L.(Pic)]Pic2.nH2O where; (Ln3+ = Pr3+, Nd3+, and Dy3+), (L = 221-cryptand), (Pic = Picrate anion), (n = 1,2 or 7). In these complexes one picrate anion is coordinated to the metal ion, also through the phenolic oxygen and the oxygen from the ortho nitro group, thus the metal ions in the cryptand complexes have a coordination number of (9).
Neural Network For The Estimation Of Ammonia Concentration In Breath Of Kidne...IOSR Journals
Neural networks are an extremely powerful tool for data mining. They are especially useful in cases
involving data classification where it is difficult to establish a pattern in the search space. In an era when
artificial intelligence is increasingly being utilised in industrial and medical applications throughout the world,
it is becoming evident that this is an emerging trend. This paper explores the idea of artificial intelligence by
employing the use of a feed-forward neural network with two process layers to determine the concentration of
ammonia in exhaled human breath. The human mouth contains many kinds of substances both in liquid and
gaseous form. The individual concentrations of each of these substances could provide useful insight to the
health condition of the entire body. Ammonia is one of such substances whose concentration in the mouth has
revealed the presence or absence of diseases in the body. Kidney failure is one diesease which is identified by
an extremely high ammonia content in human breath. This disease is as a result of the kidneys’ inability to
process the body’s liquid waste. The result of this is the release of urea throughout the body which is dissipated
in the form of ammonia through oral breath. The neural simulation is carried out using NeuroSolutions version
5 software. The neural network correctly identified the concentration of oral ammonia as an indication of
kidney failure with an accuracy of 85%.
Fluorescence technique involves the optical detection and spectral analysis of light emitted by a substance undergoing a transition from an excited electronic state to a lower electronic state. The aim of this study is to assess the -amino levulinic acid (-ALA) uptake. Based on image processing technique, Matlab was used to analyze the fluorescence images resulted from activation of (-ALA) and follow its uptake along one week. Analyzing the RGB colours pixel profile from obtained results showed different profiles for malignant tissues, normal tissues, treated just after PDT and finally at one week post PDT. The treated tissues fluorescence profile showed changes from closer to malignant tissue profile till been closed to normal one.
Factor analysis as a tool for evaluation of spatial and temporal variations i...IOSR Journals
In this case study, factor analysis was applied for evaluation of temporal/spatial variations in the
groundwater quality of Aravakurichi block, Karur district, Tamil Nadu, India. This statistical technique was
employed for the better interpretation of large complex water quality data set obtained from twenty five
groundwater locations in four seasons during the year 2012. The water samples were characterized for the
physico-chemical parameters such as pH, total alkalinity, electrical conductivity, total hardness, calcium ions,
magnesium ions, total dissolved solids, fluorides, chlorides and sulphates. Factor analysis indicated four factors
initially and when rotation of the factor axis was executed, it yielded two factors with clear indication of high
loadings for some variable and low loadings for others, facilitating data interpretation in terms of original
variables. Overall, this case study demonstrated the effectiveness of factor analysis to identify marker variables
for assessing the chemistry of groundwater besides earmarking representative sampling stations to undertake
suitable water quality management in a shortest possible time.
Perishable Inventory Model Having Weibull Lifetime and Time Dependent DemandIOSR Journals
In this paper we develop and analyse an inventory model for deteriorating items with Weibull rate of decay and time dependent demand. Using the differential equations, the instantaneous state of inventory at time‘t’, the amount of deterioration etc. are derived. With suitable cost considerations the total cost function and profit rate function are also obtained by maximizing the profit rate function, the optimal ordering and pricing policies of the model are derived. The sensitivity of the model with respect to the parameters is discussed through numerical illustration. It is observed that the deteriorating parameters have a tremendous influence on the optimal selling price and ordering quantity.
To Study the Efficacy of Electromyographic Biofeedback Training on Dynamic Eq...IOSR Journals
Abstract: Cerebral palsy (CP) is caused by static lesion to a developing nervous system that primarily affects
motor function. Spastic motor involvement is characteristic of most of these individual.Dynamicequinus is a
common deformity that worsens the ambulatory ability of both diplegic and hemiplegic conditions. The use of
electromyographic (EMG) biofeedback has been suggested as a training tool to improve the ability to increase
activation of weak and partially paralyzed muscles and to decrease the activation of muscles affected by spasm
or spasticity without regard to specific diagnosis. However, very few studies have reported the effects of EMG
biofeedback on ankle function among children with spastic cerebral palsy .Objectives of the study was to
increase the activation of tibialis anterior and to improve the functional ambulation.40 subjects were made part
of the study on the basis of inclusion and exclusion criteria divided into two groups group A and B.Group A
received traditional physical therapy exercises and electromypgraphic biofeedback and group B received only
exercise program.The treatment duration was for 4weeks 3 sessions a week.The results were analysed using
statistical tests that were paired and unpaired t-test and mannwhitneytest.The results showed significant
improvement in the pre and post treatment.The conclusion of the study lended a favourable outlook to use
biofeedback training in treatment of CP children, to improve functional ambulation and gait. Keywords: Cerebral palsy, dynamic equinus deformity, gait, electromyography, biofeedback.
Effect of Regular Exercise on Prolactin Secretion: A Pilot StudyIOSR Journals
Abstract:
Introduction: Evidence suggested that exercise may affects release of prolactin hormone. Participation in
exercise may increase secretion of prolactin hormone and may give sharp decrease in secretion of prolactin and
not only that published work demanded that there is no effect of exercise on secretion of prolactin. In this
context the researcher intend to know whether exercise affects positively or negatively or not on the release of
prolactin hormone. Aim: Determine whether participation in exercise may increase the level of secretion of
prolactine hormone or not. Method: Only two female students 29 years aged were participated in this study.
They were regularly practiced yogic asana and pranayam for 1 hour per day in the evening, 6 days per week,
for 8 weeks. The level of prolactin hormone was assessed by CLI method. In the present study all the
measurements were done at the baseline and 8 weeks of exercise training. Simple percentage calculated from
the mean value to see the quantitative changes in secretion of prolactin due to participation in the exercise
training. Result: Pre test mean was 5.80 and post test mean was 17.63 which imply that 203.96% increase in
secretion of prolactin significantly. Discussion and Conclusion: Level of secretion increased may be due to
multiple neural pathways that influence PRL secretion converges on the hypothalamus from other parts of the
brain; the effect of exercise on the secretion of PRL may also reflect the action of different neural inputs on the
activity of the hypothalamic–pituitary axis.
Key word: Exercise; Prolactin.
Quantum communication and quantum computingIOSR Journals
Abstract: The subject of quantum computing brings together ideas from classical information theory, computer
science, and quantum physics. This review aims to summarize not just quantum computing, but the whole
subject of quantum information theory. Information can be identified as the most general thing which must
propagate from a cause to an effect. It therefore has a fundamentally important role in the science of physics.
However, the mathematical treatment of information, especially information processing, is quite recent, dating
from the mid-20th century. This has meant that the full significance of information as a basic concept in physics
is only now being discovered. This is especially true in quantum mechanics. The theory of quantum information
and computing puts this significance on a firm footing, and has led to some profound and exciting new insights
into the natural world. Among these are the use of quantum states to permit the secure transmission of classical
information (quantum cryptography), the use of quantum entanglement to permit reliable transmission of
quantum states (teleportation), the possibility of preserving quantum coherence in the presence of irreversible
noise processes (quantum error correction), and the use of controlled quantum evolution for efficient
computation (quantum computation). The common theme of all these insights is the use of quantum
entanglement as a computational resource.
Keywords: quantum bits, quantum registers, quantum gates and quantum networks
Mathematical Modelling: A Comparatively Mathematical Study Model Base between...IOSR Journals
In this paper, we have studied on the topic of „Corruption‟. Also, I will try to find or study the effect of corruption on the Development of the country or any country of the world. Therefore, how find the solution of the problem of corruption will be destroyed completely from the society. We have observed that the Development of the country depends upon Corruption. That is, when the Corruption increases, Development decreases automatically of any country of the world. Therefore, I will try to find the formula on the problem of „Relation between the Corruption and Development of any field or any country of the world‟. Also, I have to highlight the concept of „Application of Mathematical modeling in the interesting problem “corruption” in every field of our country or world .Also, Applied Mathematics focuses on the formulation and study of Mathematical Models .Thus the activity of Applied Mathematics is vitally connected with Research in Pure Mathematics. So I will try to study on it and find, what is corruption and quantity of corruption and also find the growth of corruption and how it will decay? Now we convert this areal world problem to mathematics problem and find some formulae on it such as Mathematical Corruption Growth formula, Mathematical Constant corruption level formula and Mathematical decay of corruption formula.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, 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.
Derivation and Application of Six-Point Linear Multistep Numerical Method for...IOSR Journals
A six-step Continuous Block method of order (5, 5, 5, 5, 5, 5) T is proposed for direct solution of the second (2nd) order initial value problems. The main method and additional ones are obtained from the same continuous interpolant derived through interpolation and collocation procedures. The methods are derived by interpolating the continuous interpolant at 𝑥 = 𝑥𝑛+𝑗 , 𝑗 = 6 and collocating the first and second derivative of the
continuous interpolant at 𝑥𝑛+𝑗 , 𝑗 = 0 and 𝑗 = 2, 3, … 5 respectively. The stability properties of the methods are discussed and the stability region shown. The methods are then applied in block form as simultaneous numerical integrators. Two numerical experiments are given to illustrate the efficiency of the new methods.
International Journal of Mathematics and Statistics Invention (IJMSI) inventionjournals
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.
Multi objective predictive control a solution using metaheuristicsijcsit
The application of multi objective model predictive control approaches is significantly limited with
computation time associated with optimization algorithms. Metaheuristics are general purpose heuristics
that have been successfully used in solving difficult optimization problems in a reasonable computation
time. In this work , we use and compare two multi objective metaheuristics, Multi-Objective Particle
swarm Optimization, MOPSO, and Multi-Objective Gravitational Search Algorithm, MOGSA, to generate
a set of approximately Pareto-optimal solutions in a single run. Two examples are studied, a nonlinear
system consisting of two mobile robots tracking trajectories and avoiding obstacles and a linear multi
variable system. The computation times and the quality of the solution in terms of the smoothness of the
control signals and precision of tracking show that MOPSO can be an alternative for real time
applications.
On solving fuzzy delay differential equationusing bezier curves IJECEIAES
In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear fuzzy delay differential equations process is accurate and efficient. Numerical example is explained and analyzed involved first order linear fuzzy delay differential equations to demonstrate these proper features of this proposed problem.
A Computationally Efficient Algorithm to Solve Generalized Method of Moments ...Waqas Tariq
Generalized method of moment estimating function enables one to estimate regression parameters consistently and efficiently. However, it involves one major computational problem: in complex data settings, solving generalized method of moments estimating function via Newton-Raphson technique gives rise often to non-invertible Jacobian matrices. Thus, parameter estimation becomes unreliable and computationally inefficient. To overcome this problem, we propose to use secant method based on vector divisions instead of the usual Newton-Raphson technique to estimate the regression parameters. This new method of estimation demonstrates a decrease in the number of non-convergence iterations as compared to the Newton-Raphson technique and provides reliable estimates.
Continuous models of economy adopted to either define evolutions of economic
systems or investigate economic dynamics, amongst its other areas of applications, are
known to be related to differential equations. The considered model in this article takes
the form of a second order non-linear ordinary differential equation (ODE) which is
conventional solved by reducing to the system of first order. This approach is
computationally tasking, unlike block methods which bypasses reduction by directly
solving the model. A new approach is introduced named Modified Taylor Series
Approach (MTSA). Hence, the resultant MTSA-derived block method is implemented to
solve the second order non-linear model of economy under consideration.
A Class of Continuous Implicit Seventh-eight method for solving y’ = f(x, y) ...AI Publications
In this article, we develop a continuous implicit seventh-eight method using interpolation and collocation of the approximate solution for the solution of y’ = f(x, y) with a constant step-size. The method uses power series as the approximate solution in the derivation of the method. The independent solution was then derived by adopting block integrator. The properties of the method was investigated and found to be zero stable, consistent and convergent. The integrator was tested on numerical examples ranging from linear problem, Prothero-Robinson Oscillatory, Growth Model and Sir Model. The results show that the computed solution is closer to the exact solution and also, the absolutes errors perform better than the existing methods.
Uncertain Systems Order Reduction by Aggregation Method Yayah Zakaria
In the field of control engineering, approximating the higher-order system with its reduced model copes with more intricateproblems. These complex problems are addressed due to the usage of computing technologies and advanced algorithms. Reduction techniques enable the system from higherorder to lower-order form retaining the properties of former even after reduction. This document renders a method for demotion of uncertain systems based on State Space Analysis. Numerical examples are illustrated to show the accuracy of the proposed method.
Uncertain Systems Order Reduction by Aggregation Method IJECEIAES
In the field of control engineering, approximating the higher-order system with its reduced model copes with more intricateproblems. These complex problems are addressed due to the usage of computing technologies and advanced algorithms. Reduction techniques enable the system from higherorder to lower-order form retaining the properties of former even after reduction. This document renders a method for demotion of uncertain systems based on State Space Analysis. Numerical examples are illustrated to show the accuracy of the proposed method.
A Study on Differential Equations on the Sphere Using Leapfrog Methodiosrjce
In this article, a new method of analysis of the differential equations on the sphere using Leapfrog
method is presented. To illustrate the effectiveness of the Leapfrog method, an example of the differential
equations on the sphere has been considered and the solutions were obtained using methods taken taken from
the literature [17] and Leapfrog method. The obtained discrete solutions are compared with the exact solutions
of the differential equations on the sphere. Solution graphs for the differential equations on the sphere have
been presented in the graphical form to show the efficiency of this Leapfrog method. This Leapfrog method can
be easily implemented in a digital computer and the solution can be obtained for any length of time
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Chebyshev Collocation Approach for a Continuous Formulation of Implicit Hybrid Methods for Vips In Second Order Odes
1. IOSR Journal of Mathematics (IOSR-JM)
e-ISSN: 2278-5728,p-ISSN: 2319-765X, Volume 6, Issue 4 (May. - Jun. 2013), PP 09-12
www.iosrjournals.org
www.iosrjournals.org 9 | Page
Chebyshev Collocation Approach for a Continuous Formulation
of Implicit Hybrid Methods for Vips In Second Order Odes
R.B. Adeniyi1
, E.O. Adeyefa2
1
Department Of Mathematics, University Of Ilorin, Ilorin, Nigeria.
2
Department Of Mathematics/Statistics, Federal University Wukari, Taraba State, Nigeria.
Abstract: In this paper, an implicit one-step method for numerical solution of second order Initial Value
Problems of Ordinary Differential Equations has been developed by collocation and interpolation technique.
The one-step method was developed using Chebyshev polynomial as basis function and, the method was
augmented by the introduction of offstep points in order to bring about zero stability and upgrade the order of
consistency of the new method. An advantage of the derived continuous scheme is that it can produce several
outputs of solution at the off-grid points without requiring additional interpolation. Numerical examples are
presented to portray the applicability and the efficiency of the method.
Keywords:Interpolation, Chebyshev polynomial, Collocation,continuous scheme.
I. Introduction
The general second order Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) of
the form:
)1(],[,)(,)('),',,('' baxyayzayyyxfy oo
where f is continuous in [a,b], is often encountered in areas such as satellite tracking/warning systems,
celestial mechanics, mass action kinetics, solar systems and molecular biology [1]. Many of such problems may
not be easily solved analytically, hence numerical schemes are developed to solve (1). These equations are
usually reduced to a system of two first order ODEs and numerical methods for first order differential equations
are used to solve it. For such systems of first order ODEs, Linear Multistep Methods (LMMs) are powerful
numerical methods.
Some researchers have attempted the solution of (1) using LMMs without reduction to system of first
order ODEs. They include [2], [3], [4], [5] to mention a few. [6], proposed a continuous scheme based on
collocation which was found to have better error estimate and provided approximation at all interior points of
the interval of consideration. The main setback of the scheme proposed by [6] is in the need to develop
computer sub-programs needed to initialize the starting values; hence, much time is lost and the cost of
implementation is high. In view of these disadvantages, many researchers concentrated efforts on advancing the
numerical solution of IVPs in ODEs. One of the outcomes is the development of a class of methods called Block
method. The method, which shall briefly be discussed in the next section simultaneously generates
approximations at different grid points in the interval of integration and is less expensive in terms of the number
of function evaluations compared to the LMMs or Runge-Kutta methods.
II. Block Methods
Block methods are formulated in terms of LMMs. They provide the traditional advantage of one-step
methods, e.g., Runge-Kutta methods, of being self-starting and permitting easy change of step length [7].
Another important feature of the block approach is that all the discrete schemes are of uniform order and are
obtained from a single continuous formula in contrast to the non-self starting predictor-corrector approach.
In what now immediately follows, we shall develop the new method with Chebyshev polynomial as basis
function.
III. Development Of The Method
In this section, we intend to derive a continuous representation of a one-step method which will be used
to generate the main method and other methods required to set up the block method. We set out by
approximating the analytical solution of problem (1) with a Chebyshev polynomial of the form:
k
j
jj xyxTaxY
0
)2()()()(
on the partition
a = x0<xI< … <xn< xn+1< …<xN = b
on the integration interval [a,b], with a constant step size h, given by h = xn+1 – xn; n = 0, 1, …, N-1.
2. Chebyshev Collocation Approach For A Continuous Formulation
www.iosrjournals.org 10 | Page
Convectionally, we need to interpolate at at least two points to be able to approximate (1) and, to make this
happen, we proceed by arbitrarily selecting an offstep point, xn+v, vϵ(0,1), in (xn, xn+1) in such a manner that the
zero-stability of the main method is guaranteed. Then (2) is interpolated at xn+i, i = 0, v and its second derivative
is collocated at xn+i, i = 0, v and 1 so as to obtain a system of five equations each of degree four i.e. k = 4 as
follows:
4
0
''
4
0
)4()',,()(
)3()()(
j
jj
j
ijj
yyxfxTa
xyxTa
In what follows, let us arbitrarily set
2
1
v . Then, collocating (4) at
2
1
1,0, andixx in , and
interpolating (3) at
2
1
0, andixx in lead to a system of equations written in the matrix form AX = B as:
)5(
320961600
6401600
320961600
10101
11111
1
2
2
1
2
2
1
4
3
2
1
0
n
n
n
n
n
fh
fh
fh
y
y
a
a
a
a
a
Equation (5) is solved by Gaussian elimination method to obtain the value of the unknown parameters
aj, j= 0 (1) 4 as follows:
)6(
768384768
192192
19296
5
192
19248
5
64
256128
7
256
1
2
2
1
22
4
2
1
2
3
1
2
2
1
22
2
1
2
2
1
22
2
11
1
2
2
1
22
2
10
n
n
n
nn
n
n
n
n
n
nn
n
n
n
n
n
f
h
f
h
f
h
a
f
h
f
h
a
f
h
f
h
f
h
a
f
h
f
h
f
h
yya
f
h
f
h
f
h
ya
Substituting (6) into (2) yields a continuous implicit hybrid one-step method in the form:
1
0 2
1
2
1
2
2
1
2
10 )7())()(()()()(
j
n
jnj
n
n fxfxhyxyxxY
where )()( xandx jj are continuous coefficients, )( jhxyy njn is the numerical approximation of
the analytical solution at jnx and ).,,( '
jnjnjnjn yyxff
Equation (7) yields the parameters j and j as the following continuous function of t:
.
2
)8(
)2(
96
)(
)65(
48
)(
)23(
96
)(
1)(
)(
43
2
1
42
2
2
1
43
2
0
2
1
0
nxxvand
h
hv
twhere
ttt
h
t
ttt
h
t
ttt
h
t
tt
tt
Evaluating (7) at 1nx , the main method is obtained as:
)9()10(
48
2
2
11
2
2
11 n
n
n
n
nn fff
h
yyy
3. Chebyshev Collocation Approach For A Continuous Formulation
www.iosrjournals.org 11 | Page
To derive the block method, additional equations are needed since equation (9) alone will not be sufficient for
the solution at
2
1
n
x and 1nx to be obtained simultaneously. The additional methods can be obtained from
evaluating the first derivative of equation (7):
1
0 2
1
'
2
1
'
2
1
'
2
1
'
0
'
)10())()((])()([
1
)(
j
n
jnj
n
n fxfxhyxyx
h
xY
at 1
2
1,
n
n
n xandxx respectively. This yields the following discrete derivative schemes:
)13()269(969648
)12()310(969648
)11()76(969648
2
11
2
2
1
'
1
2
11
2
2
1
'
2
1
2
11
2
2
1
'
n
n
nn
n
n
n
n
nn
nn
n
n
nn
n
n
fffhyyhy
fffhyyhy
fffhyyhy
Equations (9), (11), (12) and (13) are then solved simultaneously to obtain the following explicit results:
)14(
)4(
6
)85(
24
)2(
6
)67(
962
1
1
2
1
''
1
1
2
1
''
2
1
2
1
2
'
1
1
2
1
2
'
2
1
n
n
nnn
n
n
nn
n
n
nnnn
n
n
nnn
n
fff
h
yy
fff
h
yy
ff
h
hyyy
fff
h
hyyy
IV. Numerical Examples
We consider here two test problems for the efficiency and accuracy of the one-step method
implemented as a block method.
]5[:
)exp(1)(:
1.0,1)0(',0)0(,'''.1
Source
xxySolutionExact
hyyyy
]8[:
)exp()(:
05.0,1)0(',1)0(,01000'1001''.2
Source
xxySolutionExact
hyyyyy
Table 1a: Showing the exact solutions and the computed results from the proposed methods for problem
1
X Exact Solution The New Method(TNM)
0.1 -0.105170918 -0.105170902
0.2 -0.221402758 -0.221402723
0.3 -0.349858807 -0.34985857
0.4 -0.491824697 -0.491824433
0.5 -0.64872127 -0.648720974
0.6 -0.8221188 -0.822118466
0.7 -1.013752707 -1.013752329
0.8 -1.225540928 -1.225540498
0.9 -1.459603111 -1.45960262
1.0 -1.718281828 -1.718281267
Table 1b: Comparing the absolute errors in The New Method (TNM) to error in [5] in problem 1
X Error in TNM, p=4, k=1 Error in [5],p=4, k=2
0.1 0.160756E-07 0.87931600E-04
0.2 0.351602E-07 0.32671800-03
0.3 0.237576E-06 0.22155640E-02
0.4 0.2646413E-06 0.48570930E-02
0.5 0.2967001E-06 0.90977340E-02
4. Chebyshev Collocation Approach For A Continuous Formulation
www.iosrjournals.org 12 | Page
0.6 0.3343905E-06 0.14391394E-01
0.7 0.3784705E-06 0.21437918E-01
0.8 0.4304925E-06 0.29898724E-01
0.9 0.4911569E-06 0.40300719E-01
1.0 0.561459E-06 0.52552130E-01
V. Table of Results
Table 2a: Showing the exact solutions and the computed results from the proposed methods for problem
2
X Exact Solution The New Method
0.1 0.90483742E+00 0.90483742+00
0.2 0.81873075E+00 0.81873075E+00
0.3 0.74081822E+00 0.74081822E+00
0.4 0.67032005E+00 0.67032005E+00
0.5 0.60653066E+00 0.60653066E+00
0.6 0.54881163E+00 0.54881164E+00
0.7 0.49658530E+00 0.49658530E+00
0.8 0.44932896E+00 0.44932896E+00
0.9 0.40656965E+00 0.40656966E+00
1.0 0.36787944E+00 0.36787944E+00
Table 2b: Comparing the absolute errors in the New Method to error in [8] in problem 2
X Error in TNM, p=4, k=1 Error in [8],p=6, k=5
0.1 0.23596E-09 0.698677E-11
0.2 0.47798E-09 0.100275E-11
0.3 0.58172E-09 0.785878E-11
0.4 0.73564E-09 0.104778E-10
0.5 0.81263E-09 0.632212E-10
0.6 0.89403E-09 0.100508E-10
0.7 0.99141E-09 0.936336E-11
0.8 0.101722E-08 0.264766E-11
0.9 0.10406E-08 0.106793E-10
1.0 0.107144E-08 0.232731E-10
VI. Conclusion
The desirable property of a numerical solution is to behave like the theoretical solution of the problem
which can be seen in the result above. It is obvious from TABLE 1 that the new method is more efficient and
accurate. However, even though the multiple finite difference method of [8] seemed to have produced a better
results at most of the points of evaluation in TABLE 2b, it should be noticed that the method had step number k
= 5 against the new method of step number k = 1.
Also, the investigation, through the new method reveals the viability of this approach to solve higher order
problems. In view of this, we intend to extend the work to step number k = 2 and also consider more offstep
points.
References
[1] Aladeselu, V.A., Improved family of block method for special second orderinitial value problems (I.V.Ps). Journal of the Nigerian
Association ofMathematical Physics, 11, 2007,153-158.
[2] Lambert, J.D., Numerical Methods for Ordinary Differential Systems(John Wiley, New York, 1991).
[3] Kayode S. J., An Improved Numerov method for Direct Solution of GeneralSecond Order Initial Value Problems of Ordinary
Equations, National MathsCentre proceedings 2005.
[4] Adesanya, A.O., Anake T.A. and Oghonyon, G.J., Continuous implicit method for the solution of general second order ordinary
differential equations. J. Nig. Assoc. of Math. Phys. 15, 2009, 71-78.
[5] Yahaya, Y. A. and Badmus, A. M., A Class of Collocation Methods for General Second Order Ordinary Differential Equations.
African Journal ofMathematics and Computer Science research vol. 2(4), 2009, 069-072.
[6] Awoyemi, D.O., A class of Continuous Methods for general second orderinitial value problems in ordinary differential equation.
International Journal of Computational Mathematics, 72, 1999, 29-37.
[7] Lambert, J.D., Computational Methods in Ordinary Differential Equations. John Wiley, New York, 1973.
[8] Jator, S.N., A Sixth Order Linear Multistep Method for the Direct Solutionof y'' = f(x, y, y’). International Journal of Pure and
Applied Mathematics,40(4), 2007, 457-472.