The structure-preserving property, in both the time domain and the frequency domain, is an important index for evaluating validity of a numerical method. Even in the known structure-preserving methods such as the symp...The structure-preserving property, in both the time domain and the frequency domain, is an important index for evaluating validity of a numerical method. Even in the known structure-preserving methods such as the symplectic method, the inherent conser- vation law in the frequency domain is hardly conserved. By considering a mathematical pendulum model, a Stormer-Verlet scheme is first constructed in a Hamiltonian frame- work. The conservation law of the StSrmer-Verlet scheme is derived, including the total energy expressed in the time domain and periodicity in the frequency domain. To track the structure-preserving properties of the Stormer-Verlet scheme associated with the con- servation law, the motion of the mathematical pendulum is simulated with different time step lengths. The numerical results illustrate that the StSrmer-Verlet scheme can preserve the total energy of the model but cannot preserve periodicity at all. A phase correction is performed for the StSrmer-Verlet scheme. The results imply that the phase correction can improve the conservative property of periodicity of the Stormer-Verlet scheme.展开更多
基金the National Natural Science Foundation of China(Nos.11672241,11372253,and 11432010)the Astronautics Supporting Technology Foundation of China(No.2015-HT-XGD)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment(Nos.GZ1312 and GZ1605)
文摘The structure-preserving property, in both the time domain and the frequency domain, is an important index for evaluating validity of a numerical method. Even in the known structure-preserving methods such as the symplectic method, the inherent conser- vation law in the frequency domain is hardly conserved. By considering a mathematical pendulum model, a Stormer-Verlet scheme is first constructed in a Hamiltonian frame- work. The conservation law of the StSrmer-Verlet scheme is derived, including the total energy expressed in the time domain and periodicity in the frequency domain. To track the structure-preserving properties of the Stormer-Verlet scheme associated with the con- servation law, the motion of the mathematical pendulum is simulated with different time step lengths. The numerical results illustrate that the StSrmer-Verlet scheme can preserve the total energy of the model but cannot preserve periodicity at all. A phase correction is performed for the StSrmer-Verlet scheme. The results imply that the phase correction can improve the conservative property of periodicity of the Stormer-Verlet scheme.
