This paper is concerned with a fourth-order exponential wave integrator Fourier pseudo-spectral method for solving the Klein–Gordon equation. We suggest a new numerical integration formula to approximate the time integral term in the phase space. The error estimate shows the suggested numerical method is fourth-order accurate in time and spectral accurate in space. The theoretical findings are confirmed by numerical experiments.

中文翻译：

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Klein-Gordon方程的四阶指数波积分器傅里叶伪谱方法

本文涉及解决Klein-Gordon方程的四阶指数波积分器Fourier伪谱方法。我们建议一个新的数值积分公式来近似相空间中的时间积分项。误差估计表明所建议的数值方法在时间上是四阶准确的，在空间上是频谱准确的。理论发现通过数值实验得到了证实。