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Application of the St?rmer–Verlet-Like Symplectic Method to the Wave Equation* |
| QIU Yu-Fen, WU Xin** |
School of Science, Nanchang University, Nanchang 330031
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QIU Yu-Fen, WU Xin 2013 Chin. Phys. Lett. 30 080203 |
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Abstract A fourth-order three-stage symplectic integrator similar to the second-order St?rmer–Verlet method has been proposed and used before [Chin. Phys. Lett. 28 (2011) 070201; Eur. Phys. J. Plus 126 (2011) 73]. Continuing the work initiated in the publications, we investigate the numerical performance of the integrator applied to a one-dimensional wave equation, which is expressed as a discrete Hamiltonian system with a fourth-order central difference approximation to a second-order partial derivative with respect to the space variable. It is shown that the St?rmer–Verlet-like scheme has a larger numerical stable zone than either the St?rmer–Verlet method or the fourth-order Forest–Ruth symplectic algorithm, and its numerical errors in the discrete Hamiltonian and numerical solution are also smaller.
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Received: 08 May 2013
Published: 21 November 2013
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| PACS: |
02.70.-c
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(Computational techniques; simulations)
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02.60.-x
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(Numerical approximation and analysis)
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45.10.-b
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(Computational methods in classical mechanics)
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