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

Abstract We introduce a family of high-order time semi-discretizations for semilinear wave equations of Klein–Gordon type with arbitrary smooth nonlinearities 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 based on Gauss summation which was previously developed by the authors.