Abstract
We investigate conservative properties of Runge–Kutta methods for Hamiltonian partial differential equations. It is shown that multi-symplecitic Runge–Kutta methods preserve precisely the norm square conservation law. Based on the study of accuracy of Runge–Kutta methods applied to ordinary and partial differential equations, we present some results on the numerical accuracy of conservation laws of energy and momentum for Hamiltonian PDEs under Runge–Kutta discretizations.
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J. Hong, S. Jiang and C. Li are supported by the Director Innovation Foundation of ICMSEC and AMSS, the Foundation of CAS, the NNSFC (No. 19971089, No. 10371128, No. 60771054) and the Special Funds for Major State Basic Research Projects of China 2005CB321701.
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Hong, J., Jiang, S. & Li, C. Accuracy of classical conservation laws for Hamiltonian PDEs under Runge–Kutta discretizations. Numer. Math. 112, 1–23 (2009). https://doi.org/10.1007/s00211-008-0204-4
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DOI: https://doi.org/10.1007/s00211-008-0204-4