Bernoulli Wavelets Operational Matrices Method for the Solution of Nonlinear Stochastic Itô-Volterra Integral Equations

Abstract

This article gives an effective strategy to solve nonlinear stochastic Itô-Volterra integral equations (NSIVIE). These equations can be reduced to a system of nonlinear algebraic equations with unknown coefficients, using Bernoulli wavelets, their operational matrix of integration (OMI), stochastic operational matrix of integration (SOMI) and these equations can be solved numerically. Error analysis of the proposed method is given. Moreover, the results obtained are compared to exact solutions with numerical examples to show that the method described is accurate and precise.