scholarly journals Convergence Analysis and Numerical Study of a Fixed-Point Iterative Method for Solving Systems of Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Na Huang ◽  
Changfeng Ma
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Nonlinear Equations ◽  
Convergence Theorem ◽  
Numerical Study ◽  
Numerical Results ◽  
Systems Of Nonlinear Equations ◽  
Fixed Point Iterative Method

We present a fixed-point iterative method for solving systems of nonlinear equations. The convergence theorem of the proposed method is proved under suitable conditions. In addition, some numerical results are also reported in the paper, which confirm the good theoretical properties of our approach.

scholarly journals New Modification of Fixed Point Iterative Method for Solving Nonlinear Equations

2015 ◽  
Vol 06 (11) ◽  
pp. 1857-1863 ◽  
Author(s):  
Muhammad Saqib ◽  
Muhammad Iqbal ◽  
Shahzad Ahmed ◽  
Shahid Ali ◽  
Tariq Ismaeel
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Nonlinear Equations ◽  
Fixed Point Iterative Method

scholarly journals On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Jukkrit Daengsaen ◽  
Anchalee Khemphet
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Rate Of Convergence ◽  
Convergence Theorem ◽  
Computational Cost ◽  
Closed Intervals ◽  
Iteration Methods ◽  
Nondecreasing Functions ◽  
New Iterative Method

We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.

scholarly journals Analysis of a New Fractional Model for Damped Bergers’ Equation

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 35-41 ◽  
Author(s):  
Jagdev Singh ◽  
Devendra Kumar ◽  
Maysaa Al Qurashi ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Numerical Results ◽  
Fractional Model ◽  
Applied Method ◽  
The Stability

AbstractIn this article, we present a fractional model of the damped Bergers’ equation associated with the Caputo-Fabrizio fractional derivative. The numerical solution is derived by using the concept of an iterative method. The stability of the applied method is proved by employing the postulate of fixed point. To demonstrate the effectiveness of the used fractional derivative and the iterative method, numerical results are given for distinct values of the order of the fractional derivative.

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 Approximating fixed points of demicontractive mappings by iterative methods defined as admissible perturbations

2016 ◽  
Vol 25 (1) ◽  
pp. 121-126
Author(s):  
CRISTINA TICALA ◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Convergence Theorems ◽  
Admissible Perturbation ◽  
Demicontractive Operator ◽  
Demicontractive Mappings ◽  
Fixed Point Iterative Method

The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces.

scholarly journals A Preconditioned Iterative Method for Solving Systems of Nonlinear Equations Having Unknown Multiplicity

Algorithms ◽  
2017 ◽  
Vol 10 (1) ◽  
pp. 17 ◽  
Author(s):  
Fayyaz Ahmad ◽  
Toseef Bhutta ◽  
Umar Shoaib ◽  
Malik Zaka Ullah ◽  
Ali Alshomrani ◽  
...  
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
Preconditioned Iterative

Approximating fixed points of demicontractive mappings by iterative methods defined as admissible perturbations

2016 ◽  
Vol 25 (1) ◽  
pp. 121-126
Author(s):  
CRISTINA TICALA ◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Convergence Theorems ◽  
Admissible Perturbation ◽  
Demicontractive Operator ◽  
Demicontractive Mappings ◽  
Fixed Point Iterative Method

The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces.

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