A Novel Study Based on Shifted Jacobi Polynomials to Find the Numerical Solutions of Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion

Abstract The main objective of this article is to represent an efficient numerical approach based on shifted Jacobi polynomials to solve nonlinear stochastic differential equations driven by fractional Brownian motion. In this method, function approximation and operational matrices based on shifted Jacobi polynomials have been studied, which are further used with appropriate collocation points to reduce nonlinear stochastic differential equations driven by fractional Brownian motion into a system of algebraic equations. Newton’s method has been used to solve this nonlinear system of equations, and the desired approximate solution is achieved. Moreover, the error and convergence analysis of the presented method are also established in detail. Additionally, the applicability of the proposed method is demonstrated by solving some numerical examples.