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Algebraic dynamics algorithm: Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

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Abstract

Based on the exact analytical solution of ordinary differential equations, a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm. A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models. The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision, and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.

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Authors and Affiliations

  1. Center of Theoretical Physics, Sichuan University, Chengdu, 610064, China

    Wang ShunJin & Zhang Hua

Authors
  1. Wang ShunJin
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  2. Zhang Hua
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Corresponding author

Correspondence to Wang ShunJin.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 10375039 and 90503008), the Doctoral Program Foundation from the Ministry of Education of China, and the Center of Nuclear Physics of HIRFL of China

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Wang, S., Zhang, H. Algebraic dynamics algorithm: Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm. SCI CHINA SER G 50, 53–69 (2007). https://doi.org/10.1007/s11433-007-2016-4

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  • DOI: https://doi.org/10.1007/s11433-007-2016-4

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