Sun, Geng Symplectic partitioned Runge-Kutta methods. (English) Zbl 0789.65049 J. Comput. Math. 11, No. 4, 365-372 (1993). 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 \(1 \leq s \leq 4\). Reviewer: H.Brunner (St.John’s) Cited in 38 Documents 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 Keywords:partitioned Runge-Kutta method; Hamiltonian systems; symplectic; \(W\)- transformation Citations:Zbl 0533.65041 PDFBibTeX XMLCite \textit{G. Sun}, J. Comput. Math. 11, No. 4, 365--372 (1993; Zbl 0789.65049)