A second-order Magnus-type integrator for evolution equations with delay
Numerical Analysis
2022-07-04 v2 Numerical Analysis
Functional Analysis
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.
Cite
@article{arxiv.2202.04194,
title = {A second-order Magnus-type integrator for evolution equations with delay},
author = {Petra Csomós and Dávid Kunszenti-Kovács},
journal= {arXiv preprint arXiv:2202.04194},
year = {2022}
}