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Symplectic partitioned Runge-Kutta methods. (English) Zbl 0789.65049

The author derives (sufficient) conditions for a partitioned Runge-Kutta (PRK) method used to integrate Hamiltonian systems to be symplectic. These results and the corresponding characterization of such methods are based on the \(W\)-transformation introduced by E. Hairer and G. Wanner [SIAM J. Numer. Anal. 18, 1098-1108 (1981; Zbl 0533.65041)]. As an illustration, a special class of PRK methods with \(s\) stages and order \(p = s\) is given explicitly for \(1 \leq s \leq 4\).

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
70H05 Hamilton’s equations
34A34 Nonlinear ordinary differential equations and systems

Citations:

Zbl 0533.65041
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