Abstract

We propose a Deuflhard-type exponential integrator Fourier pseudo-spectral (DEI-FP) method for solving the “Good” Boussinesq (GB) equation. The numerical scheme is based on a Deuflhard-type exponential integrator and a Fourier pseudo-spectral method for temporal and spatial discretizations, respectively. The scheme is fully explicit and efficient due to the fast Fourier transform. Rigorous error estimates are established for the method without any CFL-type condition constraint. In more details, the method converges quadratically and spectrally in time and space, respectively. Extensive numerical experiments are reported to confirm the theoretical analysis and to demonstrate rich dynamics of the GB equation.

中文翻译：

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“好” Boussinesq方程的Deuflhard型指数积分傅里叶伪谱方法

摘要

我们提出一种Deuflhard型指数积分器傅里叶伪谱（DEI-FP）方法来求解“良好”的Boussinesq（GB）方程。数值方案基于分别用于时间和空间离散化的Deuflhard型指数积分器和Fourier伪谱方法。由于快速的傅立叶变换，该方案是完全明确和有效的。为该方法建立了严格的误差估计，而没有任何CFL类型的条件约束。更详细地，该方法分别在时间和空间上平方和频谱收敛。据报道，广泛的数值实验证实了理论分析并证明了GB方程的丰富动力学。