| Algebraic dynamics algorithm:Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm |
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| 作者姓名： | WANG ShunJin & ZHANG Hua Center of Theoretical Physics Sichuan University Chengdu China |
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| 作者单位： | WANG ShunJin & ZHANG Hua Center of Theoretical Physics，Sichuan University，Chengdu 610064，China |
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| 基金项目： | 国家自然科学基金;高等学校博士学科点专项科研项目 |
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| 摘 要： | 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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| 收稿时间： | 19 September 2005 |
| 修稿时间： | 10 July 2006 |
Algebraic dynamics algorithm: Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm |
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| WANG ShunJin & ZHANG Hua Center of Theoretical Physics,Sichuan University,Chengdu ,China.Algebraic dynamics algorithm:Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm[J].Science in China(Physics Astronomy),2007,50(1):53-69. |
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| Authors: | Wang ShunJin Zhang Hua |
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| Institution: | Center of Theoretical Physics,Sichuan University,Chengdu 610064,China |
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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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| Keywords: | algebraic dynamics algorithm for ordinary differential equations preserving both geometrical and dynamical fidelity numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm |
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