Algebraic dynamics algorithm: Numerical comparison with Runge–Kutta algorithm and symplectic geometric algorithm
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 al...
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| Vydané v: | Science China. Physics, mechanics & astronomy Ročník 50; číslo 1; s. 53 - 69 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Beijing
Springer Nature B.V
01.02.2007
Center of Theoretical Physics,Sichuan University,Chengdu 610064,China |
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| ISSN: | 1672-1799, 1674-7348, 1862-2844, 1869-1927 |
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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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| AbstractList | 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. Submit Time: 2005-2-25 16:08:06 O1; 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. 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. |
| Author | Zhang, Hua Wang, ShunJin |
| AuthorAffiliation | Center of Theoretical Physics,Sichuan University,Chengdu 610064,China |
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| DOI | 10.1007/s11433-007-2016-4 |
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| Keywords | algebraic dynamics algorithm for ordinary differential equations numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm preserving both geometrical and dynamical fidelity |
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| SubjectTerms | Algebra Algorithms Controllability Differential equations Dynamical systems Exact solutions Geometric algorithms Runge-Kutta method Taylor series |
| Title | Algebraic dynamics algorithm: Numerical comparison with Runge–Kutta algorithm and symplectic geometric algorithm |
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