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On the Numerical Solution of Singular Integral Equation with Degenerate Kernel Using Laguerre Polynomials
Department of Mathematics, Umm Al-Qura University, Macca, Saudi Arabia
Department of Mathematics, University College in Qunfudah, Umm Al-Qura University, Macca, Saudi Arabia
- 1 Department of Mathematics, Umm Al-Qura University, Macca, Saudi Arabia
- 2 Department of Mathematics, University College in Qunfudah, Umm Al-Qura University, Macca, Saudi Arabia
American Journal of Computational Mathematics·Volume 13 (2023)·Pages 153–160·Published 9 January 2023·DOI10.4236/ajcm.2023.131007
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Abstract
In this paper, we derive a simple and efficient matrix formulation using Laguerre polynomials to solve the singular integral equation with degenerate kernel. This method is based on replacement of the unknown function by truncated series of well known Laguerre expansion of functions. This lead s to a system of algebraic equations with Laguerre coefficients. Thus, by solving the matrix equation, the coefficients are obtained. Some numerical examples are included to demonstrate the validity and applicability of the proposed method.
KeywordsSingular Integral EquationProjection MethodGalerkin MethodLa-guerre Polynomials
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