Open Access
Research Article
A novel approach based on the Muntz-Legendre polynomials for solving a class of the generalized Abel integral equations
S. R. Kaafir.kaafi@sutech.ac.irDepartment of Mathematics Shiraz University of TechnologyShiraz, IranView full profile → , E. Hesameddinihesameddini@sutech.ac.irDepartment of Mathematics Shiraz University of TechnologyShiraz, IranView full profile → , *P. MokhtaryCorresponding authormokhtary@sut.ac.irDepartment of Mathematics Sahand University of TechnologyTabriz, IranView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Mar 2022
- Published Online:
- 01 Jan 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1324
- Pages:
- 17–39
Abstract
This work is about a suitable numerical method based on the Muntz-Legendre polynomials for solving a type of the generalized Abel integral equations. The propose method approximates the unknown function with the Muntz-Legendre polynomials. To do this, we apply these functions and using Muntz-Galerkin method for the numerical solutions of this problem. Also, the stability and uniqueness of the solution by this scheme will be shown. Moreover, the convergence of this algorithm will be proved by preparing some theorems. Several numerical examples are presented to show the superiority and efficiency of current method.
Keywords
Subject Classifications
65M6065M1234A45
References
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