An Euler–Maruyama method and its fast implementation for multiterm fractional stochastic differential equations

Abstract

In this paper, we derive an Euler–Maruyama (EM) method for a class of multiterm fractional stochastic nonlinear differential equations and prove its strong convergence. The strong convergence order of this EM method is , where is the order of Caputo fractional derivative satisfying that , and . Then, a fast implementation of this proposed EM method is also presented based on the sum‐of‐exponentials approximation technique. Finally, some numerical experiments are given to verify the theoretical results and computational efficiency of our EM method.