Stability of the numerical solution of the periodic reaction-diffusion systems
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.
scientific article; zbMATH DE number 4005509