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arXiv · 2205.10241

Arbitrary high-order structure-preserving schemes for the generalized Rosenau-type equation

Chaolong Jiang·Xu Qian·Songhe Song·Chenxuan Zheng
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Abstract

In this paper, we are concerned with arbitrarily high-order momentum-preserving and energy-preserving schemes for solving the generalized Rosenau-type equation, respectively. The derivation of the momentum-preserving schemes is made within the symplectic Runge-Kutta method, coupled with the standard Fourier pseudo-spectral method in space. Then, combined with the quadratic auxiliary variable approach and the symplectic Runge-Kutta method, together with the standard Fourier pseudo-spectral method, we present a class of high-order mass- and energy-preserving schemes for the Rosenau equation. Finally, extensive numerical tests and comparisons are also addressed to illustrate the performance of the proposed schemes.

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Chaolong Jiang, Xu Qian, Songhe Song, Chenxuan Zheng. 2022-05-20. Arbitrary high-order structure-preserving schemes for the generalized Rosenau-type equation. https://arxiv.org/abs/2205.10241

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