On the numerical solution of weakly singular Fredholm integral equations of the second kind using Legendre wavelets

Abstract

In this paper, we present a numerical method for solving, linear and nonlinear, weakly singular Fredholm integral equations of the second kind. The method utilizes Legendre wavelets constructed on the unit interval as a basis in the Galerkin method and reduces the solution of the Fredholm integral equation to the solution of a system of algebraic equations. The features of the wavelet coefficient matrices of weakly singular kernels are studied. Finally, numerical examples are presented to show the validity and efficiency of the technique.

Keywords

Fredholm integral equation of the second kind weakly singular kernel Legendre wavelet sparse matrix

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