Rational approximation for solving Fredholm integro-differential equations by new algorithm

In this article, we used a novel semi-analytical approach, named the optimal auxiliary function method (OAFM), to solve integro-differential equations (IDEs). The OAFM includes an auxiliary function and convergence control parameters, which expedite the convergence of the method. To apply the propos...

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Bibliographic Details
Main Authors: Nawaz Rashid, Sumera, Zada Laiq, Ayaz Muhammad, Ahmad Hijaz, Awwad Fuad A., Ismail Emad A. A.
Format: Article
Language:English
Published: De Gruyter 2023-10-01
Series:Open Physics
Subjects:
Online Access:https://doi.org/10.1515/phys-2022-0181
Description
Summary:In this article, we used a novel semi-analytical approach, named the optimal auxiliary function method (OAFM), to solve integro-differential equations (IDEs). The OAFM includes an auxiliary function and convergence control parameters, which expedite the convergence of the method. To apply the proposed method, some assumptions regarding small or large parameters in the problem are necessary. We present numerical outcomes acquired via the OAFM alongside those obtained from other numerical techniques in tables. Furthermore, we demonstrate the efficacy and ease of implementing the proposed method for various IDEs using 2D graphs.
ISSN:2391-5471