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H. Mohamad and M. Oliver,
High-order uniformly accurate time integrators for semilinear wave
equations of Klein-Gordon type in the non-relativistic limit,
submitted for publication.
Abstract:
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).
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