Work

High-Order BUG Dynamical Low-Rank Integrators Based on Explicit Runge–Kutta Methods

Year: 2026

Type: article

Abstract: In this work, we introduce high-order Basis-Update & Galerkin (BUG) integrators based on explicit Runge-Kutta methods for large-scale matrix differential equations. These dynamical low-rank integrators extend the BUG integrator [1] to arbitrary explicit Runge-Kutta schemes by performing a BUG step at each stage of the method. The resulting Runge-Kutta BUG (RK-BUG) integrators are robust with respect to small singular values, fully forward in time, and high-order accurate, while enabling conservation and rank adaptivity. We prove that RK-BUG integrators retain the order of convergence of the underlying Runge-Kutta method until the error reaches a plateau corresponding to the low-rank truncation error, which vanishes as the rank becomes full. This theoretical analysis is supported by several numerical experiments. The results demonstrate the high-order convergence of the RK-BUG integrator and its superior accuracy compared to other existing dynamical low-rank integrators.

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-026-03317-5

Authors: Fabio Nobile, Sébastien Riffaud

Institution: École Polytechnique Fédérale de Lausanne

Language: English

Topic: Numerical Solvers for Ordinary Differential Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: National Science Foundation, École Polytechnique Fédérale de Lausanne, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung