Numerical approximation of nonlinear stochastic Volterra integral equation based on Walsh function

Abstract

This paper adopts a highly effective numerical approach for approximating non-linear stochastic Volterra integral equations (NLSVIEs) based on the operational matrices of the Walsh function and the collocation method. The method transforms the integral equation into a system of algebraic equations, which allows for the derivation of an approximate solution. Error analysis is performed, confirming the effectiveness of the proposed method, which results in a linear order of convergence. Numerical examples are provided to illustrate the precision and effectiveness of the proposed method.