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 - <p style="text-align: justify;">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.</p>