Stability of the numerical solution of the periodic reaction-diffusion systems
type: Item
instance of: scholarly article
title: Stability of the numerical solution of the periodic reaction-diffusion systems
zbMATH Open document ID: 0619.65086
DOI: 10.1016/0168-9274(85)90011-X
author: C. Mastroserio
author: Luciano Galeone
published in: Applied Numerical Mathematics
publication date: 1985-01-01T00:00:00Z
review text: We study the behaviour of the numerical solution of nonlinear reaction- diffusion systems, with periodic in time nonlinear term, obtained via the known \(\theta\)-method. In particular we are interested to the existence and asymptotic stability of the numerical periodic solutions in order to simulate the behaviour of the theoretical solution. To this end, by imposing the positivity of the numerical scheme, we can use some results about M-matrices. So, by means of particular over and upper solutions, we study some conditions for the stability and instability of the trivial solution. Finally we show when a positive numerical periodic solution exists and when it is unique and asymptotically stable.
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 4005509
zbMATH Keywords: theta method
zbMATH Keywords: nonlinear reaction-diffusion systems
zbMATH Keywords: asymptotic stability
zbMATH Keywords: periodic solutions
zbMATH Keywords: M-matrices
zbMATH Keywords: instability
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4005509