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
This paper deals with asymptotic behavior of solutions to a parabolic system, where two heat equations with inner absorptions are multi-coupled via inner sources and boundary flux. We determine four kinds of simultane...This paper deals with asymptotic behavior of solutions to a parabolic system, where two heat equations with inner absorptions are multi-coupled via inner sources and boundary flux. We determine four kinds of simultaneous blow-up rates under different dominations of nonlinearities in the model. Two characteristic algebraic systems associated with the problem are introduced to get very simple descriptions for the four simultaneous blow-up rates as well as the known critical exponents, respectively. It is observed that the blow-up rates are independent of the nonlinear inner absorptions.展开更多
In fluid mechanics and astrophysics,relativistic Euler equations can be used to describe the effects of special relativity which are an extension of the classical Euler equations.In this paper,we will consider the ini...In fluid mechanics and astrophysics,relativistic Euler equations can be used to describe the effects of special relativity which are an extension of the classical Euler equations.In this paper,we will consider the initial value problem of relativistic Euler equations in an initial bounded region of R N.If the initial velocity satisfies max→x 0∈∂Ω(0)N∑i=1 v_(i)^(2)(0,→x 0)<c^(2)A_(1)/2,where A 1 is a positive constant depend on some sufficiently large T^(*),then we can get the non-global existence of the regular solution for the N-dimensional relativistic Euler equations.展开更多
The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearitie...The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearities.To discretize the continuous problem in space,we utilize a spectral Galerkin method.Subsequently,we introduce a nonlinear-tamed exponential integrator scheme,resulting in a fully discrete scheme.Within the framework of semigroup theory,this study provides precise estimations of the Sobolev regularity,L^(∞) regularity in space,and Hölder continuity in time for the mild solution,as well as for its semi-discrete and full-discrete approximations.Building upon these results,we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions.A numerical example is presented to validate the theoretical findings.展开更多
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.
基金the National Natural Science Foundation of China (Grant No.10771024)
文摘This paper deals with asymptotic behavior of solutions to a parabolic system, where two heat equations with inner absorptions are multi-coupled via inner sources and boundary flux. We determine four kinds of simultaneous blow-up rates under different dominations of nonlinearities in the model. Two characteristic algebraic systems associated with the problem are introduced to get very simple descriptions for the four simultaneous blow-up rates as well as the known critical exponents, respectively. It is observed that the blow-up rates are independent of the nonlinear inner absorptions.
基金partially supported by National Science Foundation of China(No.12171305)Natural Science Foundation of Shanghai(No.20ZR1419400)。
文摘In fluid mechanics and astrophysics,relativistic Euler equations can be used to describe the effects of special relativity which are an extension of the classical Euler equations.In this paper,we will consider the initial value problem of relativistic Euler equations in an initial bounded region of R N.If the initial velocity satisfies max→x 0∈∂Ω(0)N∑i=1 v_(i)^(2)(0,→x 0)<c^(2)A_(1)/2,where A 1 is a positive constant depend on some sufficiently large T^(*),then we can get the non-global existence of the regular solution for the N-dimensional relativistic Euler equations.
基金partially supported by the National Natural Science Foundation of China(Grant No.12071073)financial support by the Jiangsu Provincial Scientific Research Center of Applied Mathematics(Grant No.BK20233002).
文摘The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearities.To discretize the continuous problem in space,we utilize a spectral Galerkin method.Subsequently,we introduce a nonlinear-tamed exponential integrator scheme,resulting in a fully discrete scheme.Within the framework of semigroup theory,this study provides precise estimations of the Sobolev regularity,L^(∞) regularity in space,and Hölder continuity in time for the mild solution,as well as for its semi-discrete and full-discrete approximations.Building upon these results,we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions.A numerical example is presented to validate the theoretical findings.
