Geodesic
Reducibility and characterization of symplectic Runge-Kutta methods
Electronic transactions on numerical analysis, Tome 2 (1994), pp. 194-204
Hamiltonian systems arise in many areas of physics, mechanics, and engineering sciences as well as in pure and applied mathematics. To their symplectic integration certain Runge-Kuttatype methods are profitably applied (see Sanz-Serna and Calvo [10]). In this paper Runge-Kutta and partitioned Runge-Kutta methods are considered. Different features of symmetry are distinguished using reflected and transposed methods. The property of DJ-irreducibility ensures symplectic methods having nonvanishing weights. A characterization of symplectic methods is deduced, from which many attributes of such methods and hints for their construction follow. Order conditions up to order four can be checked easily by simplifying assumptions. For symplectic singly-implicit Runge-Kutta methods the order barrier is shown to be two.
Classification : 65L06
Keywords: Hamiltonian system, symplectic method, Runge-Kutta and partitioned Runge- Kutta method, DJ-reducibility 
@article{ETNA_1994__2__a0,
     author = {G\"ortz,  Peter and Scherer,  Rudolf},
     title = {Reducibility and characterization of symplectic {Runge-Kutta} methods},
     journal = {Electronic transactions on numerical analysis},
     pages = {194--204},
     year = {1994},
     volume = {2},
     zbl = {0852.65061},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1994__2__a0/}
}
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AU  - Scherer,  Rudolf
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%A Scherer,  Rudolf
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%J Electronic transactions on numerical analysis
%D 1994
%P 194-204
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Görtz,  Peter; Scherer,  Rudolf. Reducibility and characterization of symplectic Runge-Kutta methods. Electronic transactions on numerical analysis, Tome 2 (1994), pp. 194-204. http://geodesic.mathdoc.fr/item/ETNA_1994__2__a0/