Invariant regions and asymptotic behaviour for the numerical solution of reaction-diffusion systems by a class of alternating direction methods

DOI10.1007/BF02576537zbMath0574.65111MaRDI QIDQ1063405

M. Montrone, C. Mastroserio

Publication date: 1984

Published in: Calcolo (Search for Journal in Brave)

zbMATH Keywords

asymptotic behaviournonlinear reaction-diffusion equationsalternating direction methodstime-independent error estimate

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12)

Related Items (2)

Stability of the numerical solution of the periodic reaction-diffusion systems ⋮ Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes

Cites Work

• Stability of invariant regions for an alternating direction method for systems of nonlinear reaction-diffusion equations
• Asymptotic stability and critical points for nonlinear quasimonotone parabolic systems
• Convergence to equilibrium states for a reaction-diffusion system modelling the spatial spread of a class of bacterial and viral diseases
• A general formulation of alternating direction methods. I: Parabolic and hyperbolic problems
• The Use of Positive Matrices for the Analysis of the Large Time Behavior of the Numerical Solution of Reaction-Diffusion Systems
• Alternating Direction Methods for Nonlinear Time-Dependent Problems
• Conservation de la positivité lors de la discrétisation des problèmes d'évolution paraboliques
• Stability and Convergence of Finite Difference Methods for Systems of Nonlinear Reaction-Diffusion Equations
• Alternating Direction Methods for Parabolic Systems in m Space Variables
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