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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Vydáno v:Science China. Physics, mechanics & astronomy Ročník 50; číslo 1; s. 53 - 69
Hlavní autoři: Wang, ShunJin, Zhang, Hua
Médium: Journal Article
Jazyk:angličtina
Vydáno: Beijing Springer Nature B.V 01.02.2007
Center of Theoretical Physics,Sichuan University,Chengdu 610064,China
Témata:
Algebra
Algorithms
Controllability
Differential equations
Dynamical systems
Exact solutions
Geometric algorithms
Runge-Kutta method
Taylor series
algebraic dynamics algorithm for ordinary differential equations
numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm
preserving both geometrical and dynamical fidelity
ISSN:1672-1799, 1674-7348, 1862-2844, 1869-1927
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Shrnutí: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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ISSN:1672-1799
1674-7348
1862-2844
1869-1927
DOI:10.1007/s11433-007-2016-4