In this paper, using the concatenating method, a series of local structure-preserving algorithms are obtained for the Klein-Gordon-Zakharov equation, including four multisymplectic algorithms, four local energy-preser...In this paper, using the concatenating method, a series of local structure-preserving algorithms are obtained for the Klein-Gordon-Zakharov equation, including four multisymplectic algorithms, four local energy-preserving algorithms, four local momentumpreserving algorithms;of these, local energy-preserving and momentum-preserving algorithms have not been studied before. The local structure-preserving algorithms mentioned above are more widely used than the global structure-preserving algorithms, since local preservation algorithms can be preserved in any time and space domains, which overcomes the defect that global preservation algorithms are limited to boundary conditions. In particular, under appropriate boundary conditions, local preservation laws are global preservation laws.Numerical experiments conducted can support the theoretical analysis well.展开更多
In this paper, we propose a local conservation law for the Zakharov system. The property is held in any local time- space region which is independent of the boundary condition and more essential than the global energy...In this paper, we propose a local conservation law for the Zakharov system. The property is held in any local time- space region which is independent of the boundary condition and more essential than the global energy conservation law. Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the system. The merit of the proposed scheme is that the local energy conservation law can be conserved exactly in any time-space region. With homogeneous Dirchlet boundary conditions, the proposed LEP scheme also possesses the discrete global mass and energy conservation laws. The theoretical properties are verified by numerical results.展开更多
A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential tha...A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time-space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O（τ2 ＋ h2）. The theoretical properties are verified by numerical experiments.展开更多
基金supported by the National Natural Science Foundation of China(11801277,11771213,12171245)。
文摘In this paper, using the concatenating method, a series of local structure-preserving algorithms are obtained for the Klein-Gordon-Zakharov equation, including four multisymplectic algorithms, four local energy-preserving algorithms, four local momentumpreserving algorithms;of these, local energy-preserving and momentum-preserving algorithms have not been studied before. The local structure-preserving algorithms mentioned above are more widely used than the global structure-preserving algorithms, since local preservation algorithms can be preserved in any time and space domains, which overcomes the defect that global preservation algorithms are limited to boundary conditions. In particular, under appropriate boundary conditions, local preservation laws are global preservation laws.Numerical experiments conducted can support the theoretical analysis well.
基金Project supported by the National Natural Science Foundation of China(Grant No.11771213)the Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology(Grant No.2243141701090)
文摘In this paper, we propose a local conservation law for the Zakharov system. The property is held in any local time- space region which is independent of the boundary condition and more essential than the global energy conservation law. Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the system. The merit of the proposed scheme is that the local energy conservation law can be conserved exactly in any time-space region. With homogeneous Dirchlet boundary conditions, the proposed LEP scheme also possesses the discrete global mass and energy conservation laws. The theoretical properties are verified by numerical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11201169,11271195,and 41231173)the Project of Graduate Education Innovation of Jiangsu Province,China(Grant No.CXLX13 366)
文摘A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time-space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O（τ2 ＋ h2）. The theoretical properties are verified by numerical experiments.
