This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
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...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.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
基金supported by the National Natural Science Foundation of China(Grant Nos.12101525,12071403)by the Natural Science Foundation of Hunan Province of China(Grant No.2023JJ40615)+1 种基金by the Research Foundation of Education Department of Hunan Province of China(Grant No.21A0108)by the Research Initiation Fund Project of Xiangtan University(Grant No.21QDZ16).
文摘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.
