Numerical Approximation of Nonlinear Stochastic Volterra Integral Equation using Walsh Function

Abstract

This article proposes an efficient numerical method for solving nonlinear stochastic Volterra integral equations using the operational matrices of the Walsh function and the collocation method. In this method, a nonlinear stochastic Volterra integral equation is reduced to a system of algebraic equations, which are then solved to obtain an approximation of the solution. Error analysis has been performed, confirming the effectiveness of the methodology, which results in a linear order of convergence. Examples were computed to demonstrate the efficacy and precision of the method.Comment: arXiv admin note: substantial text overlap with arXiv:2305.16678, arXiv:2305.0082