An analysis of operator splitting techniques in the stiff case
type: Item
instance of: scholarly article
title: An analysis of operator splitting techniques in the stiff case
zbMATH Open document ID: 0953.65062
author: Bruno Sportisse
published in: Journal of Computational Physics
publication date: 2001-01-10T00:00:00Z
review text: Operator splitting methods are widely used in many applications, such as air pollution modeling, combustion, and reactive flows. The author regards the case where the evolution equations to be simulated are stiff. He considers systems with two operators: a stiff one and a non-stiff one. For example, a linear evolution system under a singular perturbation has the form \[ {{d z}\over{d t}} = \Biggl({A\over \varepsilon} + B \Biggr) z,\quad z(0) = z_0, \] where \(\varepsilon\) is a small positive parameter. The author shows some splitting schemes for solving of the evolution systems (``first-order'', ``second-order'' schemes). The ``first-order'' scheme has the form \[ \begin{aligned} {{d z^*}\over{d t}} = B^* z^*,\quad z^*(0) = z_0, &\quad \text{on }[0,\Delta t],\\ {{d z^{**}}\over{d t}} = B^* z^{**},\quad z^{**}(0) = z^*(\Delta t), &\quad \text{on }[0,\Delta t],\end{aligned} \] where the final value is given by \(z^{**}(\Delta t)\). The main results deals with the choice of the sequential order for the operators: the stiff operator must always be last in the splitting scheme.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 92E20
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 80A25
Mathematics Subject Classification ID: 80M20
zbMATH DE Number: 1471799
zbMATH Keywords: operator splitting
zbMATH Keywords: Air Pollution Modeling
zbMATH Keywords: combustion
zbMATH Keywords: reactive flows
zbMATH Keywords: stiff systems
zbMATH Keywords: semidiscretization
zbMATH Keywords: linear evolution system
zbMATH Keywords: singular perturbation
reviewed by: Angel B. Dishliev
describes a project that uses: ODEPACK
MaRDI profile type: Publication
full work available at URL: jcph.2000.6495
OpenAlex ID: W2062951693
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DOI: 10.1006/JCPH.2000.6495
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description: scientific article; zbMATH DE number 1471799