We are concerned with numerical approximation of the linear Klein–Gordon equation with time- and space-dependent mass. We propose an asymptotic-numerical approach as a powerful tool in the presence of very high-frequency oscillations. As we shall show, the proposed method achieves high accuracy with a very low computational cost. A numerical example and comparisons are presented to confirm the efficiency of the approach.

中文翻译：

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具有时空相关质量的线性Klein-Gordon方程的渐近数值解

我们关注线性Klein-Gordon方程与时间和空间相关的质量的数值逼近。我们提出一种渐近数值方法，作为在存在非常高频率振荡的情况下的强大工具。正如我们将要展示的，所提出的方法以非常低的计算成本实现了高精度。数值例子和比较结果证实了该方法的有效性。