SYMPLECTIC RUNGE-KUTTA METHODS OF HIGH ORDER BASED ON W-TRANSFORMATION

Kaifeng Xia; Yuhao Cong; Geng Sun

doi:10.11948/2017074

2017 Volume 7 Issue 3

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Kaifeng Xia, Yuhao Cong, Geng Sun. SYMPLECTIC RUNGE-KUTTA METHODS OF HIGH ORDER BASED ON W-TRANSFORMATION[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 1185-1199. doi: 10.11948/2017074

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Kaifeng Xia, Yuhao Cong, Geng Sun. SYMPLECTIC RUNGE-KUTTA METHODS OF HIGH ORDER BASED ON W-TRANSFORMATION[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 1185-1199. doi: 10.11948/2017074

SYMPLECTIC RUNGE-KUTTA METHODS OF HIGH ORDER BASED ON W-TRANSFORMATION

1 Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China;
2 Department of Mathematics, Shanghai University, 200041, Shanghai, China;
3 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, China

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Abstract

Abstract

In this paper, characterizations of symmetric and symplectic RungeKutta 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.
- Runge-Kutta method /
- symplectic and algebraically stable method /
- W-transformation
MSC: 65L05;65L06

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References

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