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Volume 7, Number 3, 2017, Pages 1185-1199                                                                DOI:10.11948/2017074
Symplectic Runge-Kutta methods of high order based on W-transformation
Kaifeng Xia,Yuhao Cong,Geng Sun
Keywords:Runge-Kutta method, symplectic and algebraically stable method, W-transformation.
Abstract:
      In this paper , characterizations of symmetric and symplectic Runge-Kutta methods based on the W-transformation of Hairer and Wanner are presented. Using these characterizations, we construct two families symplectic (symmetric and algebraically stable or algebraically stable) Runge-Kutta methods of high order. Methods constructed in this way and presented in this paper include and extend the known classes of high order implicit Runge-Kutta methods.
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