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

Abstract

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.