Stability of operator splitting methods for systems with indefinite operators: Reaction-diffusion systems
type: Item
instance of: scholarly article
title: Stability of operator splitting methods for systems with indefinite operators: Reaction-diffusion systems
zbMATH Open document ID: 1073.65088
author: David L. Ropp
author: John N. Shadid
published in: Journal of Computational Physics
publication date: 2005-05-12T00:00:00Z
review text: The authors present an analysis of the stability of operator-splitting methods for systems with indefinite operators, including negative definite systems with an indefinite component operator and indefinite systems. The result of this analysis demonstrates the importance of the spectral decay properties of the amplification factors of the integration of the diffusion operator. The results are used to explore the convergence and it is shown experimentally that if the method used for the diffusion then high wave number modes will pollute the solution.
reviewed by: Prabhat Kumar Mahanti
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 2167950
zbMATH Keywords: reaction diffusion problems
zbMATH Keywords: convergence
zbMATH Keywords: stability
zbMATH Keywords: operator-splitting methods
zbMATH Keywords: indefinite operators
describes a project that uses: CVODE
MaRDI profile type: Publication
full work available at URL: j.jcp.2004.09.004
OpenAlex ID: W1979156898
cites work: Q3687624
cites work: Linearly implicit splitting methods for higher space-dimensional parabolic differential equations
cites work: Q4000061
cites work: Q4421310
cites work: Stability and Convergence of the Peaceman-Rachford ADI Method for Initial-Boundary Value Problems
cites work: Contractivity results for alternating direction schemes in Hilbert spaces
cites work: Q4002473
cites work: Q5657624
cites work: Studies on the accuracy of time-integration methods for the radiation-diffusion equations
cites work: Q4010300
cites work: Studies of the accuracy of time integration methods for reaction-diffusion equations.
cites work: On the Construction and Comparison of Difference Schemes
cites work: Fractional step methods applied to a chemotaxis model
cites work: Q5611377
DOI: 10.1016/J.JCP.2004.09.004
description: scientific article; zbMATH DE number 2167950