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Volume 39 Issue 1
Jan.  2013
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Journal of Beijing University of Aeronautics and Astronautics  > 2013  >  (1): 22-26.
Liu Xiaomei, Zhou Gang, Wang Yonghong, et al. Rectifying drifts of symplectic algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2013, (1): 22-26. (in Chinese)
Citation: Liu Xiaomei, Zhou Gang, Wang Yonghong, et al. Rectifying drifts of symplectic algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2013, (1): 22-26. (in Chinese)
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Rectifying drifts of symplectic algorithm

  • 1.

    School of Mechanical and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

  • 2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

  • Received Date: 21 Oct 2011
  • Publish Date: 31 Jan 2013
    Abstract
  • Symplectic algorithm preserves the symplectic structure and laws for Hamiltonian systems compared with Runge-Kutta(RK) methods, but the point-wise numerical precision is worse for elliptic Hamiltonian systems. In order to improve it, the average statistic drift formulae of the third-order symplectic method and the fourth-order scheme were deduced. The precision was improved through compensating the drifts and step segmentation. A standard was built to find a better symplectic scheme in phase drift. The results of examples show that the third-order fractional step and symmetric symplectic algorithm(FSJS3 algorithm) is higher than the fourth-order one in phase accuracy, which is recommended for engineering application.

     

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