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
针对未配备气象传感器的全球卫星导航系统(GNSS)站缺乏实测气象参数,通常利用再分析数据、经验模型替代反演大气可降水量(PWV)的问题,定量分析地面气压(P)和加权平均温度(Tm)在反演PWV中的适用性:利用欧洲中期天气预报中心(ECMWF)发布...针对未配备气象传感器的全球卫星导航系统(GNSS)站缺乏实测气象参数,通常利用再分析数据、经验模型替代反演大气可降水量(PWV)的问题,定量分析地面气压(P)和加权平均温度(Tm)在反演PWV中的适用性:利用欧洲中期天气预报中心(ECMWF)发布的第五代再分析数据集(ERA5)、美国国家环境预报中心(NCEP)/国家大气研究中心(NCAR)再分析数据、第二代和第三代全球气压和温度模型(GPT2和GPT3)、全球格网非线性加权平均温度模型(GGNTm)计算P和Tm;然后以探空站实测气象数据为参考,评估不同P和Tm的精度及其对PWV反演的影响。结果表明:1)ERA5、NCEP、GPT2、GPT3获取P的偏差(bias)绝对值小于1 h Pa,均方根误差(RMSE)小于5.5 h Pa;2)在获取Tm方面,ERA5、NCEP、GGNTm、GPT3的bias绝对值小于2.5 K,RMSE小于5.5 K;3)将ERA5、NCEP、GPT2+GGNTm、GPT3获取的气象参数应用到PWV反演中,PWV偏差绝对值小于0.5 mm,RMSE小于3 mm。分析得出应用非实测气象参数反演的GNSS大气可降水量也可获得较高精度的结论。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.
文摘针对未配备气象传感器的全球卫星导航系统(GNSS)站缺乏实测气象参数,通常利用再分析数据、经验模型替代反演大气可降水量(PWV)的问题,定量分析地面气压(P)和加权平均温度(Tm)在反演PWV中的适用性:利用欧洲中期天气预报中心(ECMWF)发布的第五代再分析数据集(ERA5)、美国国家环境预报中心(NCEP)/国家大气研究中心(NCAR)再分析数据、第二代和第三代全球气压和温度模型(GPT2和GPT3)、全球格网非线性加权平均温度模型(GGNTm)计算P和Tm;然后以探空站实测气象数据为参考,评估不同P和Tm的精度及其对PWV反演的影响。结果表明:1)ERA5、NCEP、GPT2、GPT3获取P的偏差(bias)绝对值小于1 h Pa,均方根误差(RMSE)小于5.5 h Pa;2)在获取Tm方面,ERA5、NCEP、GGNTm、GPT3的bias绝对值小于2.5 K,RMSE小于5.5 K;3)将ERA5、NCEP、GPT2+GGNTm、GPT3获取的气象参数应用到PWV反演中,PWV偏差绝对值小于0.5 mm,RMSE小于3 mm。分析得出应用非实测气象参数反演的GNSS大气可降水量也可获得较高精度的结论。
