A numerical technique to solve linear stochastic Volterra integral equation

Abstract

This article introduces a numerical technique using Walsh function approximation and the corresponding operational matrix of integration to address linear stochastic Volterra integral equation. The main objective of the approach is to transform the integral equation into a system of algebraic equations, which is then solved to obtain an approximate solution to the specified linear stochastic Volterra integral equation. The rate of convergence of the proposed method for stochastic Volterra integral equations with Lipschitz continuous functions is discussed and the corresponding error analysis shows a linear order of convergence.  The proposed approach exhibits better precision in addressing linear stochastic Volterra integral equations relative to existing methodologies, as shown by multiple examples with readily available analytical solutions.