Application of operational matrices for solving system of linear Stratonovich Volterra integral equation

Abstract

In this paper, we give a brief review on Block pulse functions (BPFs) and obtain operational matrix and stochastic operational matrix of integration based on BPFs. Then these operational matrices are used to solve system of linear Stratonovich Volterra integral equations. By applying proposed method, the system of linear Stratonovich Volterra integral equations reduce to system of linear algebraic equations which can be solved by a convenient numerical method. Also, the error analysis is proved under several mild conditions. We show the rate of convergence is O(h). Finally, by applying this method on two examples, we demonstrate accuracy and efficiency of the proposed method. All of the numerical calculation are performed on computer using a program written in MATLAB.