A fast Euler–Maruyama method for Riemann–Liouville stochastic fractional nonlinear differential equations

Abstract

In this paper, based on the sum-of-exponentials approximation, a fast Euler–Maruyama (EM) method is constructed to solve a kind of multi-term Riemann–Liouville stochastic fractional differential equations. Then the strong convergence order min{1−αm,0.5} of the proposed EM method is proved with Riemann–Liouville fractional derivatives’ orders satisfying 0<α1<α2<⋯<αm<1. Finally, two numerical examples are given to support the theoretical results and show the powerful computational performance of the fast EM method.