Presents a study that analyzed the symplecticness, stability and asymptotic of Runge-Kutta, partitioned Runge-Kutta, and Runge-Kutta-Nystr ? m methods applied to linear Hamiltonian systems. Numerical representation of...Presents a study that analyzed the symplecticness, stability and asymptotic of Runge-Kutta, partitioned Runge-Kutta, and Runge-Kutta-Nystr ? m methods applied to linear Hamiltonian systems. Numerical representation of the problem; Results in connection to P-stability; Details of the application of backward error analysis in the study.展开更多
Based on splitting multi-symplectic structures, a new multi-symplectic scheme is proposed and applied to a nonlinear wave equation. The explicit multi-symplectic scheme of the nonlinear wave equation is obtained, and ...Based on splitting multi-symplectic structures, a new multi-symplectic scheme is proposed and applied to a nonlinear wave equation. The explicit multi-symplectic scheme of the nonlinear wave equation is obtained, and the corresponding multi-symplectic conservation property is proved. The backward error analysis shows that the explicit multi-symplectic scheme has good accuracy. The sine-Gordon equation and the Klein-Gordon equation are simulated by an explicit multi-symplectic scheme. The numerical results show that the new explicit multi-symplectic scheme can well simulate the solitary wave behaviors of the nonlinear wave equation and approximately preserve the relative energy error of the equation.展开更多
A newscheme for the Zakharov-Kuznetsov(ZK)equationwith the accuracy order of O(△t^(2)+△x+△y^(2))is proposed.The multi-symplectic conservation property of the new scheme is proved.The backward error analysis of the ...A newscheme for the Zakharov-Kuznetsov(ZK)equationwith the accuracy order of O(△t^(2)+△x+△y^(2))is proposed.The multi-symplectic conservation property of the new scheme is proved.The backward error analysis of the newmulti-symplectic scheme is also implemented.The solitary wave evolution behaviors of the Zakharov-Kunetsov equation is investigated by the new multi-symplectic scheme.The accuracy of the scheme is analyzed.展开更多
In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in R^n The equations are assumed to be of the form y^· = A（y） ＋ D（y） ＋ R（y）, where ...In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in R^n The equations are assumed to be of the form y^· = A（y） ＋ D（y） ＋ R（y）, where A（y） is the conservative part subject to （A（y）, y） = 0; D（y） is the damping part or the part describing the coexistence of damping and expanding; R（y） reflects strange phenomenon of the system. It is shown that the numerical solutions generated by the symplectic Runge-Kutta（SRK） methods with bi 〉 0 （ i = 1,..., s） have long-time approximations to the exact ones, and these methods can describe the structural properties of the quadratic energy for these systems. Some numerical experiments and backward error analysis also show that these methods are better than other methods including the general algebraically stable Runge-Kutta（RK）methods.展开更多
文摘Presents a study that analyzed the symplecticness, stability and asymptotic of Runge-Kutta, partitioned Runge-Kutta, and Runge-Kutta-Nystr ? m methods applied to linear Hamiltonian systems. Numerical representation of the problem; Results in connection to P-stability; Details of the application of backward error analysis in the study.
基金Project supported by the National Natural Science Foundation of China(Nos.11161017,11071251,and 10871099)the National Basic Research Program of China(973 Program)(No.2007CB209603)+1 种基金the Natural Science Foundation of Hainan Province(No.110002)the Scientific Research Foun-dation of Hainan University(No.kyqd1053)
文摘Based on splitting multi-symplectic structures, a new multi-symplectic scheme is proposed and applied to a nonlinear wave equation. The explicit multi-symplectic scheme of the nonlinear wave equation is obtained, and the corresponding multi-symplectic conservation property is proved. The backward error analysis shows that the explicit multi-symplectic scheme has good accuracy. The sine-Gordon equation and the Klein-Gordon equation are simulated by an explicit multi-symplectic scheme. The numerical results show that the new explicit multi-symplectic scheme can well simulate the solitary wave behaviors of the nonlinear wave equation and approximately preserve the relative energy error of the equation.
基金supported by the National Natural Science Foundation of China(No.11161017,11071251 and 11271195)the Natural Science Foundation of Hainan Province(114003)the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘A newscheme for the Zakharov-Kuznetsov(ZK)equationwith the accuracy order of O(△t^(2)+△x+△y^(2))is proposed.The multi-symplectic conservation property of the new scheme is proved.The backward error analysis of the newmulti-symplectic scheme is also implemented.The solitary wave evolution behaviors of the Zakharov-Kunetsov equation is investigated by the new multi-symplectic scheme.The accuracy of the scheme is analyzed.
文摘In this paper, we study structure-preserving algorithms for dynamical systems defined by ordinary differential equations in R^n The equations are assumed to be of the form y^· = A（y） ＋ D（y） ＋ R（y）, where A（y） is the conservative part subject to （A（y）, y） = 0; D（y） is the damping part or the part describing the coexistence of damping and expanding; R（y） reflects strange phenomenon of the system. It is shown that the numerical solutions generated by the symplectic Runge-Kutta（SRK） methods with bi 〉 0 （ i = 1,..., s） have long-time approximations to the exact ones, and these methods can describe the structural properties of the quadratic energy for these systems. Some numerical experiments and backward error analysis also show that these methods are better than other methods including the general algebraically stable Runge-Kutta（RK）methods.
