Volume 48, pp. 63-80, 2018.

Asymptotic consistent exponential-type integrators for Klein-Gordon-Schrödinger systems from relativistic to non-relativistic regimes

Simon Baumstark, Georgia Kokkala, and Katharina Schratz


In this paper we propose asymptotic consistent exponential-type integrators for the Klein-Gordon-Schrödinger system. This novel class of integrators allows us to solve the system from slowly varying relativistic up to challenging highly oscillatory non-relativistic regimes without any step size restriction. In particular, our first- and second-order exponential-type integrators are asymptotically consistent in the sense of asymptotically converging to the corresponding decoupled free Schrödinger limit system.

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Key words

highly oscillatory, Klein-Gordon-Schrödinger, asymptotic consistency, exponential-type integrators

AMS subject classifications

35C20, 65M12, 35L05

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