Tamed Stochastic Runge-Kutta-Chebyshev Methods for Stochastic Differential Equations with Non-Globally Lipschitz Coefficients
Year: 2025
Author: Yanyan Yu, Aiguo Xiao, Xiao Tang
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 4 : pp. 840–865
Abstract
In this paper, we introduce a new class of explicit numerical methods called the tamed stochastic Runge-Kutta-Chebyshev (t-SRKC) methods, which apply the idea of taming to the stochastic Runge-Kutta-Chebyshev (SRKC) methods. The key advantage of our explicit methods is that they can be suitable for stochastic differential equations with non-globally Lipschitz coefficients and stiffness. Under certain non-globally Lipschitz conditions, we study the strong convergence of our methods and prove that the order of strong convergence is 1/2. To show the advantages of our methods, we compare them with some existing explicit methods (including the Euler-Maruyama method, balanced Euler-Maruyama method and two types of SRKC methods) through several numerical examples. The numerical results show that our t-SRKC methods are efficient, especially for stiff stochastic differential equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2402-m2023-0194
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 4 : pp. 840–865
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Stochastic differential equation Non-globally Lipschitz coefficient Stiffness Explicit tamed stochastic Runge-Kutta-Chebyshev method Strong convergence.