Operator splittings and spatial approximations for evolution equations

TL;DR

This paper investigates the convergence of different operator splitting methods for evolution equations, incorporating spatial approximations, and introduces a variant of Chernoff's product formula with applications to delay differential equations.

Contribution

It introduces a new variant of Chernoff's product formula to analyze convergence of splitting methods with spatial approximation for evolution equations.

Findings

Convergence results for sequential, Strang, and weighted splitting methods.

Application of methods to abstract partial delay differential equations.

A new theoretical framework for operator splitting with spatial approximations.

Abstract

The convergence of various operator splitting procedures, such as the sequential, the Strang and the weighted splitting, is investigated in the presence of a spatial approximation. To this end a variant of Chernoff's product formula is proved. The methods are applied to abstract partial delay differential equations.