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

TL;DR

This paper introduces new exponential integrators for Klein-Gordon-Schrödinger systems that are uniformly accurate across classical to non-relativistic regimes, achieving high convergence orders without time step restrictions.

Contribution

The paper develops a novel class of asymptotic consistent exponential integrators that work uniformly across different regimes of the Klein-Gordon-Schrödinger system, with explicit error analysis.

Findings

Achieves convergence orders one and two uniformly in parameter c

No time step restrictions are needed for stability and accuracy

Establishes a relation between error constants and derivatives loss

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.