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arXiv · 2201.05339

Uniformly accurate integrators for Klein-Gordon-Schr\"odinger systems from the classical to non-relativistic limit regime

Maria Cabrera Calvo
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Abstract

In this paper we present a novel class of asymptotic consistent exponential-type integrators for Klein-Gordon-Schr\"odinger systems that capture all regimes from the slowly varying classical regime up to the highly oscillatory non-relativistic limit regime. We achieve convergence of order one and two that is uniform in $c$ without any time step size restrictions. In particular, we establish an explicit relation between gain in negative powers of the potentially large parameter $c$ in the error constant and loss in derivative.

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Maria Cabrera Calvo. 2022-01-14. Uniformly accurate integrators for Klein-Gordon-Schr\"odinger systems from the classical to non-relativistic limit regime. https://arxiv.org/abs/2201.05339

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