scholarly journals Convergence Analysis for a Modified SP Iterative Method

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Fatma Öztürk Çeliker
Keyword(s):  
Iterative Method ◽  
Convergence Analysis ◽  
Iteration Method ◽  
Data Dependence ◽  
Contraction Mappings ◽  
Dependence Result ◽  
New Iterative Method

We consider a new iterative method due to Kadioglu and Yildirim (2014) for further investigation. We study convergence analysis of this iterative method when applied to class of contraction mappings. Furthermore, we give a data dependence result for fi…xed point of contraction mappings with the help of the new iteration method.

scholarly journals Zenali Iteration Method For Approximating Fixed Point of A δZA - Quasi Contractive mappings

2021 ◽  
Vol 34 (4) ◽  
pp. 78-92
Author(s):  
Zena Hussein Maibed ◽  
Ali Qasem Thajil
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Iteration Method ◽  
Iteration Process ◽  
Data Dependence ◽  
Contraction Mappings ◽  
Analytic Proof ◽  
Numerical Example ◽  
Contractive Mappings ◽  
Dependence Result

This article will introduce a new iteration method called the zenali iteration method for the approximation of fixed points. We show that our iteration process is faster than the current leading iterations  like Mann, Ishikawa, oor, D- iterations, and *-  iteration for new contraction mappings called  quasi contraction mappings. And we  proved that all these iterations (Mann, Ishikawa, oor, D- iterations and *-  iteration) equivalent to approximate fixed points of  quasi contraction. We support our analytic proof by a numerical example, data dependence result for contraction mappings type  by employing zenali iteration also discussed.

A new modified group explicit iterative method for the numerical solution of time dependent viscous Burgers' equation

2014 ◽  
Vol 05 (02) ◽  
pp. 1350029 ◽  
Author(s):  
Jyoti Talwar ◽  
R. K. Mohanty
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Iteration Method ◽  
Burgers Equation ◽  
Time Dependent ◽  
Alternating Group ◽  
Explicit Method ◽  
Rectangular Coordinates

In this article, we discuss a new smart alternating group explicit method based on off-step discretization for the solution of time dependent viscous Burgers' equation in rectangular coordinates. The convergence analysis for the new iteration method is discussed in details. We compared the results of Burgers' equation obtained by using the proposed iterative method with the results obtained by other iterative methods to demonstrate computationally the efficiency of the proposed method.

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 A novel iterative approach for solving common fixed point problems in Geodesic spaces with convergence analysis

2021 ◽  
Vol 37 (2) ◽  
pp. 145-160
Author(s):  
THANATPORN BANTAOJAI ◽  
CHANCHAL GARODIA ◽  
IZHAR UDDIN ◽  
NUTTAPOL PAKKARANANG ◽  
PANU YIMMUANG
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Common Fixed Point ◽  
Rate Of Convergence ◽  
Convergence Analysis ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Iterative Approach ◽  
Mild Conditions ◽  
New Iterative Method

In this paper, we introduce a new iterative method for nonexpansive mappings in CAT(\kappa) spaces. First, the rate of convergence of proposed method and comparison with recently existing method is proved. Second, strong and \Delta-convergence theorems of the proposed method in such spaces under some mild conditions are also proved. Finally, we provide some non-trivial examples to show efficiency and comparison with many previously existing methods.

scholarly journals A new iteration method for the solution of third-order BVP via Green's function

2021 ◽  
Vol 54 (1) ◽  
pp. 425-435
Author(s):  
Fatma Aydın Akgun ◽  
Zaur Rasulov
Keyword(s):  
Iterative Method ◽  
Green’S Function ◽  
Green's Function ◽  
Iteration Method ◽  
Existence And Uniqueness ◽  
Necessary Conditions ◽  
Uniqueness Theorems ◽  
Exact Results ◽  
Third Order ◽  
New Iterative Method

Abstract In this study, a new iterative method for third-order boundary value problems based on embedding Green’s function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.

scholarly journals Applications of Normal S-Iterative Method to a Nonlinear Integral Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Faik Gürsoy
Keyword(s):  
Integral Equation ◽  
Iterative Method ◽  
Mixed Type ◽  
Nonlinear Integral Equation ◽  
Data Dependence ◽  
Dependence Result ◽  
Fredholm Functional

It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven.

scholarly journals A Picard-S iterative method for approximating fixed point of weak-contraction mappings

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2829-2845 ◽  
Author(s):  
Faik Gürsoy
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Mixed Type ◽  
Nonlinear Integral Equation ◽  
Data Dependence ◽  
Weak Contraction ◽  
Dependence Result ◽  
Fredholm Functional

We study the convergence analysis of a Picard-S iterative method for a particular class of weakcontraction mappings and give a data dependence result for fixed points of these mappings. Also, we show that the Picard-S iterative method can be used to approximate the unique solution of mixed type Volterra-Fredholm functional nonlinear integral equation x (t) = F(t, x(t), ?t1,a1... ?tm,am K(t,s,x(s))ds, ?b1,a1...?bm,am H(t,s,x(s))ds). Furthermore, with the help of the Picard-S iterative method, we establish a data dependence result for the solution of integral equation mentioned above.

Sign in / Sign up

Export Citation Format

Share Document