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arXiv · 2202.04194

A second-order Magnus-type integrator for evolution equations with delay

Petra Csomós·Dávid Kunszenti-Kovács
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Abstract

We rewrite abstract delay equations to nonautonomous abstract Cauchy problems allowing us to introduce a Magnus-type integrator for the former. We prove the second-order convergence of the obtained Magnus-type integrator. We also show that if the differential operators involved admit a common invariant set for their generated semigroups, then the Magnus-type integrator will respect this invariant set as well, allowing for much weaker assumptions to obtain the desired convergence. As an illustrative example we consider a space-dependent epidemic model with latent period and diffusion.

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Petra Csomós, Dávid Kunszenti-Kovács. 2022-02-08. A second-order Magnus-type integrator for evolution equations with delay. https://arxiv.org/abs/2202.04194

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