A fixed point iterative scheme based on Green's function for numerical solutions of singular BVPs-Reference-Cited by-同舟云学术

A fixed point iterative scheme based on Green's function for numerical solutions of singular BVPs

Published:2023 Issue:12 Volume:8 Page:29517-29534
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Ahmad Junaid¹,Arshad Muhammad¹,George Reny²

Affiliation:

1. Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad-44000, Pakistan

2. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

Abstract

<abstract><p>We suggest a novel iterative scheme for solutions of singular boundary value problems (SBVPs) that is obtained by embedding Green's function into the Picard-Mann Hybrid (PMH) iterative scheme. This new scheme we call PMH-Green's iterative scheme and prove its convergence towards a sought solution of certain SBVPs. We impose possible mild conditions on the operator or on the parameters involved in our scheme to obtain our main outcome. After this, we prove that this new iterative scheme is weak $ w^{2} $-stable. Eventually, using two different numerical examples of SBVPs, we show that our new approach suggests highly accurate numerical solutions as compared the corresponding Picard-Green's and Mann-Green's iterative schemes.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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