scholarly journals A New Iterative Numerical Continuation Technique for Approximating the Solutions of Scalar Nonlinear Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-21 ◽  
Author(s):  
Grégory Antoni
Keyword(s):  
Numerical Analysis ◽  
Iterative Method ◽  
Iterative Algorithm ◽  
Nonlinear Equations ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Numerical Continuation ◽  
Stationary Type ◽  
Continuation Technique ◽  
New Iterative Method

The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.

scholarly journals A New Accurate and Efficient Iterative Numerical Method for Solving the Scalar and Vector Nonlinear Equations: Approach Based on Geometric Considerations

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Grégory Antoni
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
Accurate Solution ◽  
Extended Version ◽  
Root Finding ◽  
Newton Raphson ◽  
Stationary Type ◽  
Raphson Method

This paper deals with a new numerical iterative method for finding the approximate solutions associated with both scalar and vector nonlinear equations. The iterative method proposed here is an extended version of the numerical procedure originally developed in previous works. The present study proposes to show that this new root-finding algorithm combined with a stationary-type iterative method (e.g., Gauss-Seidel or Jacobi) is able to provide a longer accurate solution than classical Newton-Raphson method. A numerical analysis of the developed iterative method is addressed and discussed on some specific equations and systems.

scholarly journals On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
H. Montazeri ◽  
F. Soleymani ◽  
S. Shateyi ◽  
S. S. Motsa
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
The Other ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Tests ◽  
Programming Package ◽  
New Iterative Method

We consider a system of nonlinear equationsF(x)=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.

scholarly journals An Efficient and Straightforward Numerical Technique Coupled to Classical Newton’s Method for Enhancing the Accuracy of Approximate Solutions Associated with Scalar Nonlinear Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Grégory Antoni
Keyword(s):  
Approximate Solution ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Input Data ◽  
Numerical Technique ◽  
Nonlinear Function ◽  
Numerical Procedure ◽  
Approximate Solutions ◽  
First Order

This study concerns the development of a straightforward numerical technique associated with Classical Newton’s Method for providing a more accurate approximate solution of scalar nonlinear equations. The proposed procedure is based on some practical geometric rules and requires the knowledge of the local slope of the curve representing the considered nonlinear function. Therefore, this new technique uses, only as input data, the first-order derivative of the nonlinear equation in question. The relevance of this numerical procedure is tested, evaluated, and discussed through some examples.

scholarly journals New Iterative Method for the Solution of Fractional Damped Burger and Fractional Sharma-Tasso-Olver Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Mohammad Jibran Khan ◽  
Rashid Nawaz ◽  
Samreen Farid ◽  
Javed Iqbal
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Fractional Order ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Transform Method ◽  
Order Solution ◽  
Differential Transform ◽  
New Iterative Method ◽  
Good Agreement

The new iterative method has been used to obtain the approximate solutions of time fractional damped Burger and time fractional Sharma-Tasso-Olver equations. Results obtained by the proposed method for different fractional-order derivatives are compared with those obtained by the fractional reduced differential transform method (FRDTM). The 2nd-order approximate solutions by the new iterative method are in good agreement with the exact solution as compared to the 5th-order solution by the FRDTM.

scholarly journals New Iterative Method for Solving Nonlinear Equations

2014 ◽  
Vol 11 (4) ◽  
pp. 1649-1654 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
New Method ◽  
New Iterative Method

The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.

scholarly journals Introduction to a family of Thukral k-order method for finding multiple zeros of nonlinear equations

2017 ◽  
Vol 13 (3) ◽  
pp. 7230-7237
Author(s):  
R Thukral
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Computational Cost ◽  
Order Method ◽  
Multiple Zeros ◽  
New Iterative Method

A new one-point k-order iterative method for finding zeros of nonlinear equations having unknown multiplicity is introduced.  In terms of computational cost the new iterative method requires k+1 evaluations of functions per iteration.  It is shown that the new iterative method has a convergence of order k.

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