Convergence of a Low-Rank Strang Splitting for Stiff Matrix Differential Equations

TL;DR

This paper introduces a second-order Strang splitting method for stiff matrix differential equations with Sylvester structure, combining exact linear treatment and low-rank nonlinear integration, with proven convergence and demonstrated efficiency.

Contribution

The paper presents a novel second-order splitting scheme that effectively handles stiff matrix equations with Sylvester structure, including a rigorous convergence analysis.

Findings

The method achieves second-order accuracy under certain conditions.

Numerical experiments confirm robustness and efficiency.

The scheme effectively combines matrix exponentials with low-rank integration.

Abstract

We propose and analyze a second-order Strang splitting method for a class of stiff matrix differential equations with Sylvester-type structure. The method splits the dynamics into a stiff linear part, treated exactly via matrix exponentials, and a nonlinear part, integrated by a second-order dynamical low-rank (DLR) scheme. Our main contribution is a rigorous convergence proof showing that, under suitable assumptions, the overall scheme achieves second-order accuracy. Numerical experiments confirm the theoretical results and demonstrate the robustness and efficiency of the proposed method.