Dynamical low-rank approximation to the solution of parabolic differential equations

Dynamical low-rank approximation to the solutions of matrix differential equations leads to differential equations for the factors of a low-rank factorization of the matrices. Error bounds depending on the Lipschitz constant of the problem become not satisfactory in the case of parabolic problems with a linear stiff term and a smooth nonstiff nonlinearity. In this paper, we provide sharper error bounds, depending only on the Lipschitz constant of the nonstiff nonlinearity. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.