High-order uniformly accurate time integrators for semilinear wave equations of Klein-Gordon type in the non-relativistic limit

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).