In this paper,the dissipative and the forced terms of the Duffing equation are considered as the perturbations of nonlinear Hamiltonian equations and the perturbational effect is indicated by parameter ε.Firstly,base...
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In this paper,the dissipative and the forced terms of the Duffing equation are considered as the perturbations of nonlinear Hamiltonian equations and the perturbational effect is indicated by parameter ε.Firstly,based on the gradient Hamiltonian decomposition theory of vector fields,by using splitting methods,this paper constructs structure-preserving algorithms(SPAs)for the Duffing ***,according to the Liouville formula,it proves that the Jacobian matrix determinants of the SPAs are equal to that of the exact flow of the Duffing ***,considering the explicit Runge-Kutta methods,this paper finds that there is an error term of order p+1 for the Jacobian matrix *** volume evolution law of a given region in phase space is discussed for different algorithms,*** a result,the sum of Lyapunov exponents is exactly invariable for the SPAs proposed in this ***,through numerical experiments,relative norm errors and absolute energy errors of phase trajectories of the SPAs and the Heun method(a second-order Runge-Kutta method)are *** results illustrate that the SPAs are evidently better than the Heun method when ε is small or equal to zero.
Conformal symplecticity is generalized to forced-damped multi-symplectic PDEs in 1 + 1 dimensions Since,I conformal multi-symplectic property has a concise form for these equations. numerical algorithms that preserve ...
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Conformal symplecticity is generalized to forced-damped multi-symplectic PDEs in 1 + 1 dimensions Since,I conformal multi-symplectic property has a concise form for these equations. numerical algorithms that preserve this property. from a modified equations point of view. are available. In effect. the modified equations for standard multi-symplectic methods and for space-time splitting methods satisfy a conformal multi-symplectic property, and the splitting schemes exactly preserve global symplecticity in a special case. It is also shown that the splitting schemes yield incorrect rates of energy/momentum dissipation, but this IS not the case for standard multi-symplectic schemes. These methods work best. for problems where the dissipation coefficients are small, and a forced-damped semi-linear wave equation is considered as an example Published by Elsevier B.V. on behalf of IMACS.
In this paper, the dissipative and the forced terms of the Duffing equation are considered as the perturbations of nonlinear Hamiltonian equations and the perturbational effect is indicated by parameter ε. Firstly, b...
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In this paper, the dissipative and the forced terms of the Duffing equation are considered as the perturbations of nonlinear Hamiltonian equations and the perturbational effect is indicated by parameter ε. Firstly, based on the gradient- Hamiltonian decomposition theory of vector fields, by using splitting methods, this paper constructs structure-preserving algorithms （SPAs） for the Duffing equation. Then, according to the Liouville formula, it proves that the Jacobian matrix determinants of the SPAs are equal to that of the exact flow of the Duffing equation. However, considering the explicit Runge Kutta methods, this paper finds that there is an error term of order p＋l for the Jacobian matrix determinants. The volume evolution law of a given region in phase space is discussed for different algorithms, respectively. As a result, the sum of Lyapunov exponents is exactly invariable for the SPAs proposed in this paper. Finally, through numerical experiments, relative norm errors and absolute energy errors of phase trajectories of the SPAs and the Heun method （a second-order Runge-Kutta method） are compared. Computational results illustrate that the SPAs are evidently better than the Heun method when e is small or equal to zero.
A partially structure-preserving method for sparse symmetric matrices is proposed. Computational results on the permanents of adjacency matrices arising from molecular chemistry are presented. The largest adjacency ma...
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A partially structure-preserving method for sparse symmetric matrices is proposed. Computational results on the permanents of adjacency matrices arising from molecular chemistry are presented. The largest adjacency matrix of fullerenes computed before is that of C-60 with a cost of several hours on supercomputers, while only about 6 min on an Intel Pentium PC (1.8 GHz) with our method. Further numerical computations are given for larger fullerenes and other adjacency matrices with n = 60, 80. This shows that our method is promising for problems from molecular chemistry. (C) 2004 Elsevier B.V. All rights reserved.
Presents a study which examined the structure-preserving algorithms to phase space volume for linear dynamical systems. Preservation of phase space volume for source-free dynamical systems; Description of a volume-pre...
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Presents a study which examined the structure-preserving algorithms to phase space volume for linear dynamical systems. Preservation of phase space volume for source-free dynamical systems; Description of a volume-preserving scheme for linear system with canonical form; Information on structure-preserving schemes for linear dynamical systems.
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