Operator splitting for dissipative delay equations

TL;DR

This paper studies operator splitting methods for dissipative delay equations, analyzing convergence and order of accuracy, supported by theoretical results and numerical examples.

Contribution

It extends Lie-Trotter splitting techniques to nonlinear delay equations, providing convergence proofs and order analysis.

Findings

Convergence of the splitting method is established.

Order of convergence is characterized in detail.

Numerical illustrations demonstrate practical effectiveness.

Abstract

We investigate Lie-Trotter product formulae for abstract nonlinear evolution equations with delay. Using results from the theory of nonlinear contraction semigroups in Hilbert spaces, we explain the convergence of the splitting procedure. The order of convergence is also investigated in detail, and some numerical illustrations are presented.