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We rewrite abstract delay equations to nonautonomous abstract Cauchy problemsallowing us to introduce a Magnus-type integrator for the former. We prove thesecond-order convergence of the obtained Magnus-type integrator. We also showthat if the differential operators involved admit a common invariant set fortheir generated semigroups, then the Magnus-type integrator will respect thisinvariant set as well, allowing for much weaker assumptions to obtain thedesired convergence. As an illustrative example we consider a space-dependentepidemic model with latent period and diffusion.

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