A Galerkin solution to a regularized Cauchy singular integro-differential equation
Quarterly of Applied Mathematics
Integro-differential equation with Cauchy kernel
Journal of Computational and Applied Mathematics
A new approach to the numerical solution of weakly singular Volterra integral equations
Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Approximate solution of a class of singular integral equations of second kind
Journal of Computational and Applied Mathematics
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A method for finding the numerical solution of a weakly singular Fredholm integral equation of the second kind is presented. The Taylor series is used to remove singularity and Legendre polynomials are used as a basis. Furthermore, the Legendre function of the second kind is used to remove singularity in the Cauchy type integral equation. The integrals that appear in this method are computed in terms of gamma and beta functions and some of these integrals are computed in the Cauchy principal value sense without using numerical quadratures. Four examples are given to show the accuracy of the method.