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Dynamical low-rank approximation to the solution of parabolic differential equations. (English) Zbl 1441.37103

Summary: 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.

MSC:

37N30 Dynamical systems in numerical analysis
37M99 Approximation methods and numerical treatment of dynamical systems
65F55 Numerical methods for low-rank matrix approximation; matrix compression
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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