Comparative Study of Iterative Methods for Solving Non-Linear Equations

2021 ◽  
Vol 23 (07) ◽  
pp. 858-866
Author(s):  
Gauri Thakur ◽  
◽  
J.K. Saini ◽  
Keyword(s):  
Numerical Analysis ◽  
Iterative Methods ◽  
Linear Equations ◽  
Bisection Method ◽  
Practical Applications ◽  
Non Linear ◽  
False Position ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

In numerical analysis, methods for finding roots play a pivotal role in the field of many real and practical applications. The efficiency of numerical methods depends upon the convergence rate (how fast the particular method converges). The objective of this study is to compare the Bisection method, Newton-Raphson method, and False Position Method with their limitations and also analyze them to know which of them is more preferred. Limitations of these methods have allowed presenting the latest research in the area of iterative processes for solving non-linear equations. This paper analyzes the field of iterative methods which are developed in recent years with their future scope.

scholarly journals Rootfinding : An Iterative Tool to Solve Different Problems

2015 ◽  
Vol 5 ◽  
pp. 121-125
Author(s):  
Iswarmani Adhikari
Keyword(s):  
Numerical Analysis ◽  
Iterative Methods ◽  
Linear Equations ◽  
Secant Method ◽  
Root Finding ◽  
Non Linear ◽  
Iteration Methods ◽  
False Position ◽  
The Common ◽  
Non Linear Equations

The aim of this paper is to apply the iteration methods for the solution of non-linear equations. Among the various root finding techniques, two of the common iterative methods Regula-falsi (false position) and the Secant method are used in two different problems to show the applications of numerical analysis in different fields. The Himalayan Physics Vol. 5, No. 5, Nov. 2014 Page: 121-125

scholarly journals An Iterative Hybrid Algorithm for Roots of Non-Linear Equations

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 80-98
Author(s):  
Chaman Lal Sabharwal
Keyword(s):  
Hybrid Algorithm ◽  
Analytic Solution ◽  
Linear Equations ◽  
Root Finding ◽  
Engineering Sciences ◽  
Non Linear ◽  
False Position ◽  
Newton Raphson ◽  
And Performance ◽  
Non Linear Equations

Finding the roots of non-linear and transcendental equations is an important problem in engineering sciences. In general, such problems do not have an analytic solution; the researchers resort to numerical techniques for exploring. We design and implement a three-way hybrid algorithm that is a blend of the Newton–Raphson algorithm and a two-way blended algorithm (blend of two methods, Bisection and False Position). The hybrid algorithm is a new single pass iterative approach. The method takes advantage of the best in three algorithms in each iteration to estimate an approximate value closer to the root. We show that the new algorithm outperforms the Bisection, Regula Falsi, Newton–Raphson, quadrature based, undetermined coefficients based, and decomposition-based algorithms. The new hybrid root finding algorithm is guaranteed to converge. The experimental results and empirical evidence show that the complexity of the hybrid algorithm is far less than that of other algorithms. Several functions cited in the literature are used as benchmarks to compare and confirm the simplicity, efficiency, and performance of the proposed method.

scholarly journals MODIFIED QUADRATURE ITERATED METHODS OF BOOLE RULE AND WEDDLE RULE FOR SOLVING NON-LINEAR EQUATIONS

2021 ◽  
Vol 16 (2) ◽  
Author(s):  
Umair Khalid Qureshi
Keyword(s):  
Applied Sciences ◽  
Linear Equations ◽  
Numerical Results ◽  
Graphical Representations ◽  
Quadrature Method ◽  
Non Linear ◽  
Newton Raphson ◽  
Steffensen Method ◽  
Raphson Method ◽  
Non Linear Equations

This article is presented a modified quadrature iterated methods of Boole rule and Weddle rule for solving non-linear equations which arise in applied sciences and engineering. The proposed methods are converged quadratically and the idea of developed research comes from Boole rule and Weddle rule. Few examples are demonstrated to justify the proposed method as the assessment of the newton raphson method, steffensen method, trapezoidal method, and quadrature method. Numerical results and graphical representations of modified quadrature iterated methods are examined with C++ and EXCEL. The observation from numerical results that the proposed modified quadrature iterated methods are performance good and well executed as the comparison of existing methods for solving non-linear equations.

scholarly journals Wilkinson Polynomials: Accuracy Analysis Based on Numerical Methods of the Taylor Series Derivative

2020 ◽  
Vol 3 (2) ◽  
pp. 155-160
Author(s):  
Vera Mandailina ◽  
Syaharuddin Syaharuddin ◽  
Dewi Pramita ◽  
Malik Ibrahim ◽  
Habib Ratu Perwira Negara
Keyword(s):  
Taylor Series ◽  
Linear Equations ◽  
Computational Design ◽  
Qualitative Comparison ◽  
Comparison Results ◽  
Starting Point ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

Some of the numeric methods for solutions of non-linear equations are taken from a derivative of the Taylor series, one of which is the Newton-Raphson method. However, this is not the only method for solving cases of non-linear equations. The purpose of the study is to compare the accuracy of several derivative methods of the Taylor series of both single order and two-order derivatives, namely Newton-Raphson method, Halley method, Olver method, Euler method, Chebyshev method, and Newton Midpoint Halley method. This research includes qualitative comparison types, where the simulation results of each method are described based on the comparison results. These six methods are simulated with the Wilkinson equation which is a 20-degree polynomial. The accuracy parameters used are the number of iterations, the roots of the equation, the function value f (x), and the error. Results showed that the Newton Midpoint Halley method was the most accurate method. This result is derived from the test starting point value of 0.5 to the equation root x = 1, completed in 3 iterations with a maximum error of 0.0001. The computational design and simulation of this iterative method which is a derivative of the two-order Taylor series is rarely found in college studies as it still rests on the Newton-Raphson method, so the results of this study can be recommended in future learning.

EMAHAMAN METODE NUMERIK (STUDI KASUS METODE NEW-RHAPSON) MENGGUNAKAN PEMPROGRMAN MATLAB

2017 ◽  
Vol 1 (1) ◽  
pp. 95
Author(s):  
Siti Nurhabibah Hutagalung
Keyword(s):  
Numerical Methods ◽  
Theoretical Analysis ◽  
Nonlinear Equations ◽  
Linear Equations ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

Abstract - The study of the characteristics of non-liier functions can be carried out experimentally and theoretically. One part of theoretical analysis is computation. For computational purposes, numerical methods can be used to solve equations complicated, for example non-linear equations. There are a number of numerical methods that can be used to solve nonlinear equations, the Newton-Raphson method. Keywords - Numerical, Newton Raphson.

scholarly journals AN ITERATIVE, BRACKETING & DERIVATIVE-FREE METHOD FOR NUMERICAL SOLUTION OF NON-LINEAR EQUATIONS USING STIRLING INTERPOLATION TECHNIQUE

2021 ◽  
Author(s):  
Sanaullah Jamali
Keyword(s):  
Linear Equations ◽  
Derivative Free ◽  
Interpolation Technique ◽  
Non Linear ◽  
Derivative Free Method ◽  
Newton Raphson ◽  
Microsoft Windows ◽  
Regula Falsi Method ◽  
Raphson Method ◽  
Non Linear Equations

In this article, an iterative, bracketing and derivative-free method have been proposed with the second-order of convergence for the solution of non-linear equations. The proposed method derives from the Stirling interpolation technique, Stirling interpolation technique is the process of using points with known values or sample points to estimate values at unknown points or polynomials. All types of problems (taken from literature) have been tested by the proposed method and compared with existing methods (regula falsi method, secant method and newton raphson method) and it’s noted that the proposed method is more rapidly converges as compared to all other existing methods. All problems were solved by using MATLAB Version: 8.3.0.532 (R2014a) on my personal computer with specification Intel(R) Core (TM) i3-4010U CPU @ 1.70GHz with RAM 4.00GB and Operating System: Microsoft Windows 10 Enterprise Version 10.0, 64-Bit Server, x64-based processor.

scholarly journals Implementations of Open and Closed Method Numerically: A Non-linear Equations Solution Convergence Test

2019 ◽  
Vol 2 (2) ◽  
pp. 1
Author(s):  
Maulia Putri ◽  
Syaharuddin Syaharuddin
Keyword(s):  
Comparative Research ◽  
Linear Equations ◽  
Exponential Equation ◽  
Convergence Test ◽  
Solution Convergence ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations ◽  
Different Levels

Non-linear equations are one of the studies in mathematics. Root search in complex non-linear equations can be solved by numerical methods. Many methods to solve the equation. Therefore, the purpose of this research is to conduct simulation of closed and open methods such as Newton Raphson method, Secant method, Regula Falsi, Fixet Point, and Bisection. This is done as a form of comparative research to see the accuracy, number of iterations, and errors of each method in resolving the non-linear equations. As for the case being resolved is the roots of the exponential equation, trigonometry, logarithmic and polynomial degrees of three. The results of this study resulted in different levels of convergence in resolving each case

scholarly journals Newton-raphson method to solve systems of non-linear equations in VANET performance optimization

2019 ◽  
Vol 8 (1) ◽  
pp. 336-342
Author(s):  
Siti Asilah Yah ◽  
Naimah Yaakob ◽  
Mohamed Elshaikh Elobaid ◽  
Ong Bi Lynn ◽  
R. Badlishah ◽  
...  
Keyword(s):  
Performance Optimization ◽  
Network Performance ◽  
Ad Hoc ◽  
Linear Equations ◽  
Delivery Ratio ◽  
Medium Access ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method ◽  
Non Linear Equations

Nowadays, Vehicular Ad-Hoc Network (VANET) has got more attention from the researchers. The researchers have studied numerous topics of VANET, such as the routing protocols of VANET and the MAC protocols of VANET. The aim of their works is to improve the network performance of VANET, either in terms of energy consumption or packet delivery ratio (PDR) and delay. For this research paper, the main goal is to find the coefficient of a, b and c of three non-linear equations by using a Newton- Raphson method. Those three non-linear equations are derived from a different value of Medium Access Control (MAC) protocol's parameters. After that, those three coefficient is then will be used in optimization of the VANET in terms of energy, PDR, and delay.

scholarly journals Deprived of Second Derivative Iterated Method for Solving Nonlinear Equations

2021 ◽  
Vol 58 (2) ◽  
pp. 39-44
Author(s):  
Umair Khalid Qureshi ◽  
Sanaullah Jamali ◽  
Zubair Ahmed Kalhoro ◽  
Guan Jinrui
Keyword(s):  
Applied Sciences ◽  
Iterative Method ◽  
Graphical Representation ◽  
Linear Equations ◽  
Numerical Results ◽  
Second Derivative ◽  
Practical Applications ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method

Non-linear equations are one of the most important and useful problems, which arises in a varied collection of practical applications in engineering and applied sciences. For this purpose, in this paper has been developed an iterative method with deprived of second derivative for the solution of non-linear problems. The developed deprived of second derivative iterative method is convergent quadratically, and which is derived from Newton Raphson Method and Taylor series. The numerical results of the developed method are compared with the Newton Raphson Method and Modified Newton Raphson Method. From graphical representation and numerical results, it has been observed that the deprived of second derivative iterative method is more appropriate and suitable as accuracy and iteration perception by the valuation of Newton Raphson Method and Modified Newton Raphson Method for estimating a non-linear problem. 

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