Convergence Analysis of a Fifth-Order Iterative Method Using Recurrence Relations and Conditions on the First Derivative

2021 ◽  
Vol 18 (2) ◽  
Author(s):  
S. George ◽  
I. K. Argyros ◽  
P. Jidesh ◽  
M. Mahapatra ◽  
M. Saeed
Keyword(s):  
Iterative Method ◽  
Convergence Analysis ◽  
Recurrence Relations ◽  
First Derivative ◽  
Fifth Order

scholarly journals On some iterative methods with frozen derivatives for solving equations

2021 ◽  
Vol 5 (1) ◽  
pp. 209-217
Author(s):  
Samundra Regmi ◽  
◽  
Christopher Argyros ◽  
Ioannis K. Argyros ◽  
Santhosh George ◽  
...  
Keyword(s):  
Banach Space ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Radius Of Convergence ◽  
Numerical Examples ◽  
First Derivative ◽  
Solving Equations

We determine a radius of convergence for an efficient iterative method with frozen derivatives to solve Banach space defined equations. Our convergence analysis use \(\omega-\) continuity conditions only on the first derivative. Earlier studies have used hypotheses up to the seventh derivative, limiting the applicability of the method. Numerical examples complete the article.

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.

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