Schur Decomposition for Stiff Differential Equations
Numerical Analysis
2023-05-23 v1 Computational Engineering, Finance, and Science
Numerical Analysis
Computational Physics
Abstract
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.
Cite
@article{arxiv.2305.12488,
title = {Schur Decomposition for Stiff Differential Equations},
author = {Thoma Zoto and John C. Bowman},
journal= {arXiv preprint arXiv:2305.12488},
year = {2023}
}