Numerical solution of stochastic fractional integro-differential equation by the spectral collocation method

摘要

Fractional calculus is used to model various different phenomena in nature today. The aim of this paper is to propose the shifted Legendre spectral collocation method to solve stochastic fractional integro-differential equations (SFIDEs). In this approach, we consider the P panels M-point Newton–Cotes rules with M fixed for estimating It ô integrals. The main characteristic of the presented method is that it reduces SFIDEs into a system of algebraic equations. Thus, we can solve the problem by Newton’s method. Furthermore, the convergence analysis of the approach is considered. The method is computationally attractive, and numerical examples confirm the validity and efficiency of the proposed method.