A computational method for solving nonlinear stochastic Volterra integral equations

摘要

In this paper, an efficient method for solving nonlinear stochastic Itô–Volterra integral equations (NSIVIEs) is proposed. By using new adjustment of hat basis functions and their stochastic operational matrix of integration, the NSIVIE is reduced to a nonlinear system of algebraic equations. Also, the error analysis of the proposed method is investigated and proved that the order of convergence is O(h4). Finally, numerical examples affirm the efficiency of the proposed method.