In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P-stable, and of first algebraic order and high phase-la...In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P-stable, and of first algebraic order and high phase-lag order. To improve the algebraic order, we give a composition second order scheme with the proposed method and its adjoint. We report some numerical results to illustrate the efficiency of our methods.展开更多
In this paper,we propose an explicit symplectic Fourier pseudospectral method for solving the Klein-Gordon-Schr odinger equation.The key idea is to rewrite the equation as an infinite-dimensional Hamiltonian system an...In this paper,we propose an explicit symplectic Fourier pseudospectral method for solving the Klein-Gordon-Schr odinger equation.The key idea is to rewrite the equation as an infinite-dimensional Hamiltonian system and discrete the system by using Fourier pseudospectral method in space and symplectic Euler method in time.After composing two different symplectic Euler methods for the ODEs resulted from semi-discretization in space,we get a new explicit scheme for the target equation which is of second order in space and spectral accuracy in time.The canonical Hamiltonian form of the resulted ODEs is presented and the new derived scheme is proved strictly to be symplectic.The new scheme is totally explicitwhereas symplectic scheme are generally implicit or semi-implicit.Linear stability analysis is carried and a necessary Courant-Friedrichs-Lewy condition is given.The numerical results are reported to test the accuracy and efficiency of the proposed method in long-term computing.展开更多
基金The project is supported by NSF of Anhui Province(No.2005jk218), China.
文摘In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P-stable, and of first algebraic order and high phase-lag order. To improve the algebraic order, we give a composition second order scheme with the proposed method and its adjoint. We report some numerical results to illustrate the efficiency of our methods.
基金This work is supported by the Jiangsu Collaborative Innovation Center for Climate Change,the National Natural Science Foundation of China(Grant Nos.11271195 and 11271196)and the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘In this paper,we propose an explicit symplectic Fourier pseudospectral method for solving the Klein-Gordon-Schr odinger equation.The key idea is to rewrite the equation as an infinite-dimensional Hamiltonian system and discrete the system by using Fourier pseudospectral method in space and symplectic Euler method in time.After composing two different symplectic Euler methods for the ODEs resulted from semi-discretization in space,we get a new explicit scheme for the target equation which is of second order in space and spectral accuracy in time.The canonical Hamiltonian form of the resulted ODEs is presented and the new derived scheme is proved strictly to be symplectic.The new scheme is totally explicitwhereas symplectic scheme are generally implicit or semi-implicit.Linear stability analysis is carried and a necessary Courant-Friedrichs-Lewy condition is given.The numerical results are reported to test the accuracy and efficiency of the proposed method in long-term computing.
