This paper continues to study the explicit two-stage fourth-order accurate time discretizations[5-7].By introducing variable weights,we propose a class of more general explicit one-step two-stage time discretizations,...This paper continues to study the explicit two-stage fourth-order accurate time discretizations[5-7].By introducing variable weights,we propose a class of more general explicit one-step two-stage time discretizations,which are different from the existing methods,e.g.the Euler methods,Runge-Kutta methods,and multistage multiderivative methods etc.We study the absolute stability,the stability interval,and the intersection between the imaginary axis and the absolute stability region.Our results show that our two-stage time discretizations can be fourth-order accurate conditionally,the absolute stability region of the proposed methods with some special choices of the variable weights can be larger than that of the classical explicit fourth-or fifth-order Runge-Kutta method,and the interval of absolute stability can be almost twice as much as the latter.Several numerical experiments are carried out to demonstrate the performance and accuracy as well as the stability of our proposed methods.展开更多
This paper studies the two-stage fourth-order accurate time discretization[J.Q.Li and Z.F.Du,SIAM J.Sci.Comput.,38(2016)]and its application to the special relativistic hydrodynamical equations.Our analysis reveals th...This paper studies the two-stage fourth-order accurate time discretization[J.Q.Li and Z.F.Du,SIAM J.Sci.Comput.,38(2016)]and its application to the special relativistic hydrodynamical equations.Our analysis reveals that the new two-stage fourth-order accurate time discretizations can be proposed.With the aid of the direct Eulerian GRP(generalized Riemann problem)methods and the analytical resolution of the local“quasi 1D”GRP,the two-stage fourth-order accurate time discretizations are successfully implemented for the 1D and 2D special relativistic hydrodynamical equations.Several numerical experiments demonstrate the performance and accuracy as well as robustness of our schemes.展开更多
基金partially supported by the Special Project on Highperformance Computing under the National Key R&D Program(No.2020YFA0712002)the National Natural Science Foundation of China(No.12126302,12171227).
文摘This paper continues to study the explicit two-stage fourth-order accurate time discretizations[5-7].By introducing variable weights,we propose a class of more general explicit one-step two-stage time discretizations,which are different from the existing methods,e.g.the Euler methods,Runge-Kutta methods,and multistage multiderivative methods etc.We study the absolute stability,the stability interval,and the intersection between the imaginary axis and the absolute stability region.Our results show that our two-stage time discretizations can be fourth-order accurate conditionally,the absolute stability region of the proposed methods with some special choices of the variable weights can be larger than that of the classical explicit fourth-or fifth-order Runge-Kutta method,and the interval of absolute stability can be almost twice as much as the latter.Several numerical experiments are carried out to demonstrate the performance and accuracy as well as the stability of our proposed methods.
基金The authors were partially supported by the Special Project on High-performance Computing under the National Key R&D Program(No.2016YF B0200603)Sci-ence Challenge Project(No.JCK Y2016212A502)the National Natural Science Foundation of China(Nos.91630310&11421101).
文摘This paper studies the two-stage fourth-order accurate time discretization[J.Q.Li and Z.F.Du,SIAM J.Sci.Comput.,38(2016)]and its application to the special relativistic hydrodynamical equations.Our analysis reveals that the new two-stage fourth-order accurate time discretizations can be proposed.With the aid of the direct Eulerian GRP(generalized Riemann problem)methods and the analytical resolution of the local“quasi 1D”GRP,the two-stage fourth-order accurate time discretizations are successfully implemented for the 1D and 2D special relativistic hydrodynamical equations.Several numerical experiments demonstrate the performance and accuracy as well as robustness of our schemes.
