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Symplectic Runge-Kutta methods of high order based on W-transformation |
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| Authors: | Kaifeng Xi Yuhao Cong and Geng Sun |
| Institution: | Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China,Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China;Department of Mathematics, Shanghai University, 200041, Shanghai, China,Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, China |
| 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. |
| Keywords: | Runge-Kutta method symplectic and algebraically stable method W-transformation |
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