Expansion Method for Solving Fredholm Integral Equations

Abstract

In this paper a new method for solving the integral equation in space-time which arises in mathematical physics, mechanics and the heat conduction theory is presented. The central idea is: First, differentiating both sides of two-dimensions Fredholm integral Equations ntimes with respect to both variables x and t, second, substituting the Taylor series of two variables for the unknown function, and third, obtain a system of linear equations which can be solved by a suitable truncation scheme .Lastly,the double-quadrature rules are used to calculate the required integrals in this procedure. The presented algorithm is illustrated by some numerical examples with comparison tables.