A modified EM method and its fast implementation for multi-term Riemann-Liouville stochastic fractional differential equations

05/07/2022
by   Jingna Zhang, et al.
0

In this paper, a modified Euler-Maruyama (EM) method is constructed for a kind of multi-term Riemann-Liouville stochastic fractional differential equations and the strong convergence order min1-α_m, 0.5 of the proposed method is proved with Riemann-Liouville fractional derivatives' orders 0<α_1<α_2<...<α_m <1. Then, based on the sum-of-exponentials approximation, a fast implementation of the modified EM method which is called a fast EM method is derived to greatly improve the computational efficiency. Finally, some numerical examples are carried out to support the theoretical results and show the powerful computational performance of the fast EM method.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/29/2022

The semi-implicit Euler-Maruyama method for nonlinear non-autonomous stochastic differential equations driven by a class of Lévy processes

In this paper, we investigate the strong convergence of the semi-implici...
research
03/27/2021

EM-WaveHoltz: A flexible frequency-domain method built from time-domain solvers

A novel approach to computing time-harmonic solutions of Maxwell's equat...
research
08/25/2023

Exponential Euler method for stiff stochastic differential equations with additive fractional Brownian noise

We discuss a system of stochastic differential equations with a stiff li...
research
08/28/2022

The rate of Lp-convergence for the Euler-Maruyama method of the stochastic differential equations with Markovian switching

This work deals with the Euler-Maruyama (EM) scheme for stochastic diffe...
research
06/22/2023

A Lotka-Volterra type model analyzed through different techniques

We consider a modified Lotka-Volterra model applied to the predator-prey...
research
12/16/2021

Dual Approach as Empirical Reliability for Fractional Differential Equations

Computational methods for fractional differential equations exhibit esse...

Please sign up or login with your details

Forgot password? Click here to reset