Abstract
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 conservation law in the frequency domain is hardly conserved. By considering a mathematical pendulum model, a Störmer-Verlet scheme is first constructed in a Hamiltonian framework. The conservation law of the Störmer-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 Störmer-Verlet scheme associated with the conservation law, the motion of the mathematical pendulum is simulated with different time step lengths. The numerical results illustrate that the Störmer-Verlet scheme can preserve the total energy of the model but cannot preserve periodicity at all. A phase correction is performed for the Störmer-Verlet scheme. The results imply that the phase correction can improve the conservative property of periodicity of the Störmer-Verlet scheme.
Original language | English |
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Pages (from-to) | 1225-1232 |
Number of pages | 8 |
Journal | Applied Mathematics and Mechanics (English Edition) |
Volume | 38 |
Issue number | 9 |
DOIs | |
State | Published - 1 Sep 2017 |
Keywords
- Hamiltonian system
- mathematical pendulum
- phase correction
- structurepreserving
- Störmer-Verlet scheme
- symplectic