Generating functions of multi-symplectic RK methods via DW Hamilton–Jacobi equations

Hong, Jialin; Sun, Yajuan

doi:10.1007/s00211-008-0170-x

Cited by 7 publications

(1 citation statement)

References 23 publications

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“…For the numerical study of Hamiltonian PDEs, the multi-symplectic structure is investigated and then a lot of reliable numerical methods (e.g. [7,8,9,10,11,12,13,14]) preserving the multi-symplectic structure, for instance, muti-symplectic RK/PRK methods, collocation methods, splitting methods, spectral methods, etc., have been developed. Especially, we refer to [10,15,16,17] and references therein for the multi-symplectic methods of Hamiltonian wave equations.…”

Section: Introductionmentioning

confidence: 99%

Energy-preserving multi-symplectic Runge-Kutta methods for Hamiltonian wave equations

Chen,

Hong,

Sim

et al. 2019

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It is well-known that a numerical method which is at the same time geometric structurepreserving and physical property-preserving cannot exist in general for Hamiltonian partial differential equations. In this paper, we present a novel class of parametric multi-symplectic Runge-Kutta methods for Hamiltonian wave equations, which can also conserve energy simultaneously in a weaker sense with a suitable parameter. The existence of such a parameter, which enforces the energy-preserving property, is proved under certain assumptions on the fixed step sizes and the fixed initial condition. We compare the proposed method with the classical multi-symplectic Runge-Kutta method in numerical experiments, which shows the remarkable energy-preserving property of the proposed method and illustrate the validity of theoretical results.

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