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Chniti, C. (2013) Numerical Approximations of Fredholm Integral Equations with Abel Kernel Using Legendre and Chebychev Polynomials. Journal of Mathematical and Computational Science, 3, 655-667.

has been cited by the following article:

• TITLE: On the Numerical Solution of Singular Integral Equation with Degenerate Kernel Using Laguerre Polynomials

  AUTHORS: Khadeejah Sultan Alroogy, Musa Adam Aigo

  KEYWORDS: Singular Integral Equation, Projection Method, Galerkin Method, La-guerre Polynomials

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.13 No.1, March 23, 2023

  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 leads 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.