We introduce a family of high-order time semi-discretizations for semilinear wave equations of Klein--Gordon type with arbitrary smooth nonlinerities that are uniformly accurate in the non-relativistic limit where the speed of light goes to infinity. Our schemes do not require pre-computations that are specific to the nonlinearity and have no restrictions in step size. Instead, they rely upon a general oscillatory quadrature rule developed in a previous paper (Mohamad and Oliver, arXiv:1909.04616).

翻译：我们针对具有任意光滑非线性的克莱因-戈登型半线性波动方程，引入一族高阶时间半离散化格式。这些格式在光速趋于无穷大的非相对论极限下具有一致精确性。我们的方案无需针对非线性项进行特定的预计算，且对步长无限制条件。其核心思想依赖于前期论文（Mohamad 和 Oliver, arXiv:1909.04616）中建立的通用振荡型求积法则。