Operator splitting for nonautonomous delay equations

TL;DR

This paper develops a product formula approach for solving nonautonomous delay equations, providing convergence analysis and numerical examples to demonstrate its effectiveness.

Contribution

It introduces a general product formula for nonautonomous delay equations and analyzes convergence and error estimates.

Findings

Established convergence of the product formula solution

Derived error estimates for differentiable history functions

Validated the theoretical results with numerical examples

Abstract

We provide a general product formula for the solution of nonautonomous abstract delay equations. After having shown the convergence we obtain estimates on the order of convergence for differentiable history functions. Finally, the theoretical results are demonstrated on some typical numerical examples.