Numerical solutions of Troesch's problem based on a faster iterative scheme with an application-Reference-Cited by-同舟云学术

Numerical solutions of Troesch's problem based on a faster iterative scheme with an application

Published:2024 Issue:4 Volume:9 Page:9164-9183
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ahmad Junaid¹,Arshad Muhammad¹,Ma Zhenhua²

Affiliation:

1. Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan

2. Department of Mathematics and Physics, Hebei University of Architecture, Zhangjiakou 075024, China

Abstract

<abstract><p>The purpose of this manuscript was to introduce a new iterative approach based on Green's function for approximating numerical solutions of the Troesch's problem. A Banach space of continuous functions was considered for establishing the main outcome. First, we set an integral operator using a Green's function and embedded this new operator into a three-step iterative scheme. We proved the main convergence result with the help of some mild assumptions on the parameters involved in our scheme and in the problem. Moreover, we proved that the new iterative approach was weak $ w^{2} $-stable. The high accuracy and stability of the scheme was confirmed by several numerical simulations. As an application of the main result, we solved a class of fractional boundary value problems (BVPs). The main results improved and unified several known results of the literature.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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