The Newton-Raphson method ( also known as Newton's method) is a way to quickly find a good approximation for the root of a real-valued function f (x) = 0f (x) = 0. It uses the idea that a nonstop and differentiable function can be approached by a straight line tangent to it.
This slide includes the basic descriptions and function determinations ideas.
Numerical Study of Some Iterative Methods for Solving Nonlinear Equationsinventionjournals
Β
In this paper we introduce, numerical study of some iterative methods for solving non linear equations. Many iterative methods for solving algebraic and transcendental equations is presented by the different formulae. Using bisection method , secant method and the Newtonβs iterative method and their results are compared. The software, matlab 2009a was used to find the root of the function for the interval [0,1]. Numerical rate of convergence of root has been found in each calculation. It was observed that the Bisection method converges at the 47 iteration while Newton and Secant methods converge to the exact root of 0.36042170296032 with error level at the 4th and 5th iteration respectively. It was also observed that the Newton method required less number of iteration in comparison to that of secant method. However, when we compare performance, we must compare both cost and speed of convergence [6]. It was then concluded that of the three methods considered, Secant method is the most effective scheme. By the use of numerical experiments to show that secant method are more efficient than others.
The Newton-Raphson method ( also known as Newton's method) is a way to quickly find a good approximation for the root of a real-valued function f (x) = 0f (x) = 0. It uses the idea that a nonstop and differentiable function can be approached by a straight line tangent to it.
This slide includes the basic descriptions and function determinations ideas.
Numerical Study of Some Iterative Methods for Solving Nonlinear Equationsinventionjournals
Β
In this paper we introduce, numerical study of some iterative methods for solving non linear equations. Many iterative methods for solving algebraic and transcendental equations is presented by the different formulae. Using bisection method , secant method and the Newtonβs iterative method and their results are compared. The software, matlab 2009a was used to find the root of the function for the interval [0,1]. Numerical rate of convergence of root has been found in each calculation. It was observed that the Bisection method converges at the 47 iteration while Newton and Secant methods converge to the exact root of 0.36042170296032 with error level at the 4th and 5th iteration respectively. It was also observed that the Newton method required less number of iteration in comparison to that of secant method. However, when we compare performance, we must compare both cost and speed of convergence [6]. It was then concluded that of the three methods considered, Secant method is the most effective scheme. By the use of numerical experiments to show that secant method are more efficient than others.
This Chapter is part of previous published ch.1 and ch.3 and its use for undergraduate students in physics department. also, you can use it for mathematical and Statistical courses and for those experimental courses of data fitting.
The well-known methods' that utilized in the numerical techniques. Several examples illustrated to make the numerical methods that presented more sensible. The Excel program is utilized in this paper.
Fortran is a general-purpose programming language, mainly intended for mathematical computations in
science applications
this chapter is the third chapter
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
Β
The main purpose of this research is to find out the best method through iterative methods for solving the nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st degree based iterative methods. After that, the graphical development is established here with the help of the four iterative methods and these results are tested with various functions. An example of the algebraic equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two examples of the algebraic and transcendental equation are applied to verify the best method, as well as the level of errors, are shown graphically.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
Β
The main purpose of this research is to find out the best method through iterative methods for solving the
nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the
nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st
degree based iterative methods. After that, the graphical development is established here with the help of
the four iterative methods and these results are tested with various functions. An example of the algebraic
equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two
examples of the algebraic and transcendental equation are applied to verify the best method, as well as the
level of errors, are shown graphically.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
Β
The main purpose of this research is to find out the best method through iterative methods for solving the nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st degree based iterative methods. After that, the graphical development is established here with the help of the four iterative methods and these results are tested with various functions. An example of the algebraic equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two examples of the algebraic and transcendental equation are applied to verify the best method, as well as the level of errors, are shown graphically.
Published in association with the Utilitas Mathematica Academy. Offers selected original research in Pure and Applied Mathematics and Statistics. It enjoys a good reputation and popularity at the international level in terms of research papers and distribution worldwide.
https://utilitasmathematica.com/index.php/Index
Our Journal We believe that by embracing a wide range of backgrounds and viewpoints, we enrich the statistical discourse and enhance the quality and relevance of our research. Our commitment to inclusivity extends beyond the content of our publications.
https://utilitasmathematica.com/index.php/Index
Our Journal has a profession of statistics can only thrive when justice, equity, diversity, and inclusion are not just ideals but integral components of our ethos. We recognize that a diverse and inclusive community sparks creativity, innovation, and a richness of perspectives that is indispensable for advancing statistical knowledge.
APPROXIMATIONS; LINEAR PROGRAMMING;NON- LINEAR FUNCTIONS; PROJECT MANAGEMENT WITH PERT/CPM; DECISION THEORY; THEORY OF GAMES; INVENTORY MODELLING; QUEUING THEORY
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Β
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
This Chapter is part of previous published ch.1 and ch.3 and its use for undergraduate students in physics department. also, you can use it for mathematical and Statistical courses and for those experimental courses of data fitting.
The well-known methods' that utilized in the numerical techniques. Several examples illustrated to make the numerical methods that presented more sensible. The Excel program is utilized in this paper.
Fortran is a general-purpose programming language, mainly intended for mathematical computations in
science applications
this chapter is the third chapter
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
Β
The main purpose of this research is to find out the best method through iterative methods for solving the nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st degree based iterative methods. After that, the graphical development is established here with the help of the four iterative methods and these results are tested with various functions. An example of the algebraic equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two examples of the algebraic and transcendental equation are applied to verify the best method, as well as the level of errors, are shown graphically.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
Β
The main purpose of this research is to find out the best method through iterative methods for solving the
nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the
nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st
degree based iterative methods. After that, the graphical development is established here with the help of
the four iterative methods and these results are tested with various functions. An example of the algebraic
equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two
examples of the algebraic and transcendental equation are applied to verify the best method, as well as the
level of errors, are shown graphically.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
Β
The main purpose of this research is to find out the best method through iterative methods for solving the nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st degree based iterative methods. After that, the graphical development is established here with the help of the four iterative methods and these results are tested with various functions. An example of the algebraic equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two examples of the algebraic and transcendental equation are applied to verify the best method, as well as the level of errors, are shown graphically.
Published in association with the Utilitas Mathematica Academy. Offers selected original research in Pure and Applied Mathematics and Statistics. It enjoys a good reputation and popularity at the international level in terms of research papers and distribution worldwide.
https://utilitasmathematica.com/index.php/Index
Our Journal We believe that by embracing a wide range of backgrounds and viewpoints, we enrich the statistical discourse and enhance the quality and relevance of our research. Our commitment to inclusivity extends beyond the content of our publications.
https://utilitasmathematica.com/index.php/Index
Our Journal has a profession of statistics can only thrive when justice, equity, diversity, and inclusion are not just ideals but integral components of our ethos. We recognize that a diverse and inclusive community sparks creativity, innovation, and a richness of perspectives that is indispensable for advancing statistical knowledge.
APPROXIMATIONS; LINEAR PROGRAMMING;NON- LINEAR FUNCTIONS; PROJECT MANAGEMENT WITH PERT/CPM; DECISION THEORY; THEORY OF GAMES; INVENTORY MODELLING; QUEUING THEORY
Similar to Newton Raphson Method in numerical methods of advanced engineering mathematics (20)
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Β
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
β’ Remote control: Parallel or serial interface.
β’ Compatible with MAFI CCR system.
β’ Compatible with IDM8000 CCR.
β’ Compatible with Backplane mount serial communication.
β’ Compatible with commercial and Defence aviation CCR system.
β’ Remote control system for accessing CCR and allied system over serial or TCP.
β’ Indigenized local Support/presence in India.
β’ Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
β’ Remote control: Parallel or serial interface
β’ Compatible with MAFI CCR system
β’ Copatiable with IDM8000 CCR
β’ Compatible with Backplane mount serial communication.
β’ Compatible with commercial and Defence aviation CCR system.
β’ Remote control system for accessing CCR and allied system over serial or TCP.
β’ Indigenized local Support/presence in India.
Application
β’ Remote control: Parallel or serial interface.
β’ Compatible with MAFI CCR system.
β’ Compatible with IDM8000 CCR.
β’ Compatible with Backplane mount serial communication.
β’ Compatible with commercial and Defence aviation CCR system.
β’ Remote control system for accessing CCR and allied system over serial or TCP.
β’ Indigenized local Support/presence in India.
β’ Easy in configuration using DIP switches.
Student information management system project report ii.pdfKamal Acharya
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Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
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AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with ο¬y-by-wire ο¬ight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Forklift Classes Overview by Intella PartsIntella Parts
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Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Courier management system project report.pdfKamal Acharya
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It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Cosmetic shop management system project report.pdfKamal Acharya
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Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Vaccine management system project report documentation..pdfKamal Acharya
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The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
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Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
4. 4
As we know from school days , and still we have studied
about the solutions of equations like Quadratic equations
, Cubical equations & polynomial equations and having
roots in the form of
π₯ =
βπΒ± π2β4ππ
2π
where a, b , c are the coefficient of equation.
But nowadays it is very difficult to remember formulas
for higher degree polynomial equations . Hence to
remove these difficulties there are few numerical
methods, one of the easiest of them is Newton Raphson
Method Which has to be discussed in this power point
presentation.
Newton Raphson method is a numerical technique
which is used to find the roots of Algebraic &
transcendental Equations .
5. 6
Newton Raphson method is a numerical
technique which is used to find the roots of
Algebraic & transcendental Equations .
Algebraic Equations :
An equation of the form of quadratic or
polynomial.
e.g. π₯4+π₯2+1=0
π₯8-1 =0
π₯3-2x -5=0
6. 7
Transcendental equation :
An equation which contains some
transcendental functions Such as
exponential or trigonometric functions.
e.g. sin , cos , tan , ππ₯ , π₯π , log etc.
3x-cosx-1=0
logx+2x=0
ππ₯-3x=0
Sinx+10x-7=38
Newton Raphson Method :
Let us consider an equation π(π₯) = 0
having graphical representation as
7. 8
.
β’ f(x) =0 , is a given equation
β’ Starting from an initial point π₯0
β’ Determine the slope of f(x) at x=π₯0 .Call πβ(π₯0).
Slope ;
= tanΡ²
πβ²(
Hence ;
β’ Newton Raphson formula
Algorithm for f(x)=0
β’ Calculate fβ(x) symbolically.
8. Choose an initial guess π₯0 as given below let [a,b] be any interval such that π π < 0 πππ π π > 0
.
β’
. Similarly
.
β’ Then by repetition of this process we can find π₯3 ,π₯4 , π₯5 β¦ β¦
β’ At last we reach at a stage where we find ππ+π = ππ.
β’ Then we will stop.
β’ Hence ππ will be the required root of given equation.
NRM by Taylor series :-
if we have given an equation π(π₯) = 0.
π₯0 be the approximated root of given equation.
9. 10
β’ Let (π₯0 +h) be the actual root where βhβ is very
small such that f(π₯0 + β)=0
From Taylor series expansion on expanding to
f(π₯0 + β)
f(fβββ(π₯0) +β¦β¦.
Now on neglecting higher powers of h
f(π₯0) + hfβ(π₯0) =0
From above h=
Hence first approximation π₯1=(π₯0 + β);
10. Second approximation ;
On repeating this process
We get
This is the required newton Raphson method.
How to solve an example :
F(x)= π₯3- 2x β 5
Fβ(x) = 3π₯2-2
Now checking for initial point ;
F(3) =16
F(2)= -1
F(3) =16
Hence root lies between (2,3)
Initial point
(
From NRM formula
Putting all these above values in this
formula
11. .
12
π+1 π
π₯ = π₯ β
n n
3 x 2
ο 2
ο 2 x ο 5
π+1 π
π₯ = π₯ β
n
n n
3 x 2
ο 2
ο 2 x ο 5
x 3
On putting initial value π₯0 = 2.5
We get first approximate root;
π₯1=2.164179104
Similarly:
π₯2=2.097135356
π₯3=2.094555232
π₯4=2.094551482
π₯5=2.094551482
Hence π±π=π±π
Hence 2.094551482 is the required root of
given equation
12. 13
β’ To find the square root of any no.
β’ To find the inverse
β’ To find inverse square root.
β’ Root of any given equation.
Application of NRM :
13. 16
Limitations of NRM:
β’ Fβ(x)=0 is real disaster for this
method
β’ Fββ(x)=0 causes the solution to
diverse
β’ Sometimes get trapped in local
maxima and minima