Numerical solution of nonlinear stochastic Itô – Volterra integral equation driven by fractional Brownian motion

Abstract

Purpose

This paper aims to study fractional Brownian motion and its applications to nonlinear stochastic integral equations. Bernstein polynomials have been applied to obtain the numerical results of the nonlinear fractional stochastic integral equations.

Design/methodology/approach

Bernstein polynomials have been used to obtain the numerical solutions of nonlinear fractional stochastic integral equations. The fractional stochastic operational matrix based on Bernstein polynomial has been used to discretize the nonlinear fractional stochastic integral equation. Convergence and error analysis of the proposed method have been discussed.

Findings

Two illustrated examples have been presented to justify the efficiency and applicability of the proposed method. The corresponding obtained numerical results have been compared with the exact solutions to establish the accuracy and efficiency of the proposed method.

Originality/value

To the best of the authors’ knowledge, nonlinear stochastic Itô–Volterra integral equation driven by fractional Brownian motion has been for the first time solved by using Bernstein polynomials. The obtained numerical results well establish the accuracy and efficiency of the proposed method.

Citation

Saha Ray, S. and Singh, S. (2020), "Numerical solution of nonlinear stochastic Itô – Volterra integral equation driven by fractional Brownian motion", Engineering Computations, Vol. 37 No. 9, pp. 3243-3268. https://doi.org/10.1108/EC-01-2020-0039