A collocation method for the numerical solution of a class of linear stochastic integral equations based on Legendre polynomials

Abstract

In this paper, a collocation method will introduce. This method is applied to obtain the numerical solution of a class of linear stochastic integral equations. For this purpose, the integrals of these equations are expressed in terms of Legendre polynomials. Then they are applied to the stochastic integral equation and calculate the obtained equations at the node points, where results in a linear system that will solve by conventional methods. Finally, to evaluate the effectiveness of the proposed method, an example is provided, and the numerical results are analyzed.