Solutions of integral equations via modified Laguerre polynomials

Abstract

The Laguerre polynomial function is modified with an additional parameter and is applied to solve integral equations. First, the convolution of two modified Laguerre polynomials is developed. The dependent variables in the integral equation are assumed to be expressed by a modified Laguerre polynomial series. A set of algebraic equations is obtained from the integral equation. A recursive computational algorithm is employed to calculate the expansion coefficients. Examples are given, the results obtained from the modified Laguerre polynomials being much better than from the conventional Laguerre polynomials.