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<p>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.</p>

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

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  • 发表日期：

    2025年9月27日

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  • Haidar Mohamad,
  • Marcel Oliver

摘要

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.