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arXiv · 2008.05227

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

Haidar Mohamad·Marcel Oliver
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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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Haidar Mohamad, Marcel Oliver. 2020-08-12. High-order uniformly accurate time integrators for semilinear wave equations of Klein-Gordon type in the non-relativistic limit. https://arxiv.org/abs/2008.05227

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