Stability and Convergence of Product Formulas for Operator Matrices

TL;DR

This paper establishes verifiable conditions for the stability and convergence of product formulas like Trotter and Strang when applied to operator matrices, with applications to abstract Cauchy problems and boundary feedback systems.

Contribution

It provides new stability criteria for operator matrix splittings ensuring convergence of product formulas, extending their applicability to complex systems.

Findings

Derived easy-to-verify stability conditions.

Proved convergence of Trotter, Strang, and weighted product formulas.

Applied results to inhomogeneous Cauchy problems and boundary feedback systems.

Abstract

We present easy to verify conditions implying stability estimates for operator matrix splittings which ensure convergence of the associated Trotter, Strang and weighted product formulas. The results are applied to inhomogeneous abstract Cauchy problems and to boundary feedback systems.