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Research Article | Open Access

Applying faster algorithm for obtaining convergence, stability, and data dependence results with application to functional-integral equations

Hasanen A. Hammad1,2( ), Habib Ur Rehman3, Mohra Zayed4( )
Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi Arabia
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
Department of Mathematics, Monglkut's University of Technology, Bangkok 10140, Thailand
Mathematics Department, College of Science, King Khalid University, Abha, Saudi Arabia
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Abstract

The goal of this manuscript is to create a new faster iterative algorithm than the previous writing's sober algorithms. In the setting of Banach spaces, this algorithm is used to analyze convergence, stability, and data-dependence results. Basic numerical examples are also provided to highlight the behavior and effectiveness of our approach. Ultimately, the proposed approach is used to solve the functional Volterra-Fredholm integral problem as an application.

Keywords

convergence resultfixed pointdata-dependent resultΞ-stablenumerical experimentfunctional integral equation
CLC number: 47H10, 47A56, 65R20

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AIMS Mathematics
Volume 7 Issue 10,
October 2022
Pages 19026-19056
DOI: 10.3934/math.20221046

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Hammad HA, Ur Rehman H, Zayed M. Applying faster algorithm for obtaining convergence, stability, and data dependence results with application to functional-integral equations. AIMS Mathematics, 2022, 7(10): 19026-19056. https://doi.org/10.3934/math.20221046

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Received: 21 July 2022
Revised: 19 August 2022
Accepted: 22 August 2022
Published: 15 October 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)