Schur Decomposition for Stiff Differential Equations

A quantitative definition of numerical stiffness for initial value problems is proposed. Exponential integrators can effectively integrate linearly stiff systems, but they become expensive when the linear coefficient is a matrix, especially when the time step is adapted to maintain a prescribed loca...

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Bibliographic Details
Main Authors Zoto, Thoma, Bowman, John C
Format Journal Article
LanguageEnglish
Published 21.05.2023
Subjects
Computer Science - Computational Engineering, Finance, and Science
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
Physics - Computational Physics
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Summary:A quantitative definition of numerical stiffness for initial value problems is proposed. Exponential integrators can effectively integrate linearly stiff systems, but they become expensive when the linear coefficient is a matrix, especially when the time step is adapted to maintain a prescribed local error. Schur decomposition is shown to avoid the need for computing matrix exponentials in such simulations, while still circumventing linear stiffness.
DOI:10.48550/arxiv.2305.12488