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Volume 43, Issue 4
Tamed Stochastic Runge-Kutta-Chebyshev Methods for Stochastic Differential Equations with Non-Globally Lipschitz Coefficients

Yanyan Yu, Aiguo Xiao & Xiao Tang

DOI: 10.4208/jcm.2402-m2023-0194

J. Comp. Math., 43 (2025), pp. 840-865.

Published online: 2025-07

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  • 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.

  • Keywords

Stochastic differential equation, Non-globally Lipschitz coefficient, Stiffness, Explicit tamed stochastic Runge-Kutta-Chebyshev method, Strong convergence.

  • AMS Subject Headings

65C30, 60H10, 60H35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-43-840, author = {Yu , YanyanXiao , Aiguo and Tang , Xiao}, title = {Tamed Stochastic Runge-Kutta-Chebyshev Methods for Stochastic Differential Equations with Non-Globally Lipschitz Coefficients}, journal = {Journal of Computational Mathematics}, year = {2025}, volume = {43}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2402-m2023-0194}, url = {http://global-sci.org/intro/article_detail/jcm/24263.html} }
TY - JOUR T1 - Tamed Stochastic Runge-Kutta-Chebyshev Methods for Stochastic Differential Equations with Non-Globally Lipschitz Coefficients AU - Yu , Yanyan AU - Xiao , Aiguo AU - Tang , Xiao JO - Journal of Computational Mathematics VL - 4 SP - 840 EP - 865 PY - 2025 DA - 2025/07 SN - 43 DO - http://doi.org/10.4208/jcm.2402-m2023-0194 UR - https://global-sci.org/intro/article_detail/jcm/24263.html KW - Stochastic differential equation, Non-globally Lipschitz coefficient, Stiffness, Explicit tamed stochastic Runge-Kutta-Chebyshev method, Strong convergence. AB -

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.

Yu , YanyanXiao , Aiguo and Tang , Xiao. (2025). Tamed Stochastic Runge-Kutta-Chebyshev Methods for Stochastic Differential Equations with Non-Globally Lipschitz Coefficients. Journal of Computational Mathematics. 43 (4). 840-865. doi:10.4208/jcm.2402-m2023-0194
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