Accurate long-term integration of dynamical systems (Q1902066)
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scientific article; zbMATH DE number 815814
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Accurate long-term integration of dynamical systems |
scientific article; zbMATH DE number 815814 |
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Accurate long-term integration of dynamical systems (English)
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21 May 1996
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Properties concerning the global error of the integration performed over a very long time of a system of differential equations by symplectic or symmetric methods are studied. It is shown that the error growth -- for problems with periodic solution and for integrable systems using symplectic or symmetric methods -- is only linear in \(t_n\), compared to a quadratic error growth in the general case. A variable stepsize implementation for symmetric collocation methods is also explained.
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dynamical systems
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symmetric Runge-Kutta methods
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symplectic methods
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long-term integration
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Hamiltonian problems
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reversible systems
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error growth
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periodic solution
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integrable systems
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variable stepsize
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symmetric collocation methods
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