scholarly journals On a Novel Fourth-Order Algorithm for Solving Systems of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Diyashvir K. R. Babajee ◽  
Alicia Cordero ◽  
Fazlollah Soleymani ◽  
Juan R. Torregrosa
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Iterative Scheme ◽  
Higher Order ◽  
Numerical Results ◽  
Systems Of Nonlinear Equations ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Order Algorithm

This paper focuses on solving systems of nonlinear equations numerically. We propose an efficient iterative scheme including two steps and fourth order of convergence. The proposed method does not require the evaluation of second or higher order Frechet derivatives per iteration to proceed and reach fourth order of convergence. Finally, numerical results illustrate the efficiency of the method.

scholarly journals A Class of Steffensen-Type Iterative Methods for Nonlinear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
F. Soleymani ◽  
M. Sharifi ◽  
S. Shateyi ◽  
F. Khaksar Haghani
Keyword(s):  
Nonlinear Systems ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
New Method ◽  
Systems Of Nonlinear Equations ◽  
Numerical Tests ◽  
Frechet Derivatives ◽  
Fréchet Derivatives

A class of iterative methods without restriction on the computation of Fréchet derivatives including multisteps for solving systems of nonlinear equations is presented. By considering a frozen Jacobian, we provide a class ofm-step methods with order of convergencem+1. A new method named as Steffensen-Schulz scheme is also contributed. Numerical tests and comparisons with the existing methods are included.

scholarly journals An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 546
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Ángel Alberto Magreñán ◽  
Alejandro Moysi
Keyword(s):  
Nonlinear Equation ◽  
Weight Function ◽  
Convergence Analysis ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Higher Order ◽  
Multiple Roots ◽  
Iterative Technique ◽  
Derivative Free

In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one parameter α to achieve the fourth-order of convergence. Initially, the convergence analysis is performed for particular values of multiple roots. Afterward, it concludes in general. Moreover, the effectiveness of the presented methods are certified on some applications of nonlinear equations and compared with the earlier derivative and derivative-free schemes. The obtained results depict better performance than the existing methods.

scholarly journals Metode Iterasi Tiga Langkah untuk Menyelesaikan Persamaan NonLinear dengan Menggunakan Matlab

2019 ◽  
Vol 4 (2) ◽  
pp. 34
Author(s):  
Deasy Wahyuni ◽  
Elisawati Elisawati
Keyword(s):  
Numerical Simulations ◽  
Nonlinear Equations ◽  
Newton Method ◽  
Iteration Method ◽  
Newton's Method ◽  
Order Of Convergence ◽  
Higher Order ◽  
Convergence Order ◽  
Matlab Program ◽  
Analytical Results

Newton method is one of the most frequently used methods to find solutions to the roots of nonlinear equations. Along with the development of science, Newton's method has undergone various modifications. One of them is the hasanov method and the newton method variant (vmn), with a higher order of convergence. In this journal focuses on the three-step iteration method in which the order of convergence is higher than the three methods. To find the convergence order of the three-step iteration method requires a program that can support the analytical results of both methods. One of them using the help of the matlab program. Which will then be compared with numerical simulations also using the matlab program.  Keywords : newton method, newton method variant, Hasanov Method and order of convergence

An efficient fourth order weighted-Newton method for systems of nonlinear equations

2012 ◽  
Vol 62 (2) ◽  
pp. 307-323 ◽  
Author(s):  
Janak Raj Sharma ◽  
Rangan Kumar Guha ◽  
Rajni Sharma
Keyword(s):  
Nonlinear Equations ◽  
Newton Method ◽  
Fourth Order ◽  
Systems Of Nonlinear Equations

scholarly journals Modified Potra-Pták Multi-step Schemes with Accelerated Order of Convergence for Solving Systems of Nonlinear Equations

2018 ◽  
Vol 24 (1) ◽  
pp. 3
Author(s):  
Himani Arora ◽  
Juan Torregrosa ◽  
Alicia Cordero
Keyword(s):  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Sixth Order ◽  
Systems Of Nonlinear Equations ◽  
Order Method ◽  
Third Order ◽  
Boundary Problems ◽  
Newton Step ◽  
The Family ◽  
Efficiency And Reliability

In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order Potra-Pták method and last is weighted-Newton step. Furthermore, we generalize our work to derive a family of multi-step iterative methods with order of convergence 3 r + 6 , r = 0 , 1 , 2 , … . The sixth order method is the special case of this multi-step scheme for r = 0 . The family gives a four-step ninth order method for r = 1 . As much higher order methods are not used in practice, so we study sixth and ninth order methods in detail. Numerical examples are included to confirm theoretical results and to compare the methods with some existing ones. Different numerical tests, containing academical functions and systems resulting from the discretization of boundary problems, are introduced to show the efficiency and reliability of the proposed methods.

scholarly journals On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 891 ◽  
Author(s):  
Janak Raj Sharma ◽  
Deepak Kumar ◽  
Lorentz Jäntschi
Keyword(s):  
Order Of Convergence ◽  
Higher Order ◽  
New Method ◽  
Systems Of Nonlinear Equations ◽  
Third Order ◽  
Type Method ◽  
Cpu Time ◽  
Chebyshev’S Method ◽  
Derivative Free ◽  
Fifth Order

We propose a derivative-free iterative method with fifth order of convergence for solving systems of nonlinear equations. The scheme is composed of three steps, of which the first two steps are that of third order Traub-Steffensen-type method and the last is derivative-free modification of Chebyshev’s method. Computational efficiency is examined and comparison between the efficiencies of presented technique with existing techniques is performed. It is proved that, in general, the new method is more efficient. Numerical problems, including those resulting from practical problems viz. integral equations and boundary value problems, are considered to compare the performance of the proposed method with existing methods. Calculation of computational order of convergence shows that the order of convergence of the new method is preserved in all the numerical examples, which is not so in the case of some of the existing higher order methods. Moreover, the numerical results, including the CPU-time consumed in the execution of program, confirm the accurate and efficient behavior of the new technique.

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