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The network method for solutions of oscillating reaction-diffusion systems. (English) Zbl 0822.65059
The one-dimensional reaction-diffusion equation \(c_ t= Dc_{zz}+ f(c)\), where \(D\) is a constant, is approximated by a system of linear ordinary differential equations. It is done by discretizing the special variable \(z\), namely \(c_{i+ 1}- 2c_ i+ c_{i- 1}\) is taken instead of \((\Delta z)^ 2\cdot c_{zz}\).
Suitably interpreted the system is formally similar to an electrical network. The last one is well implemented into many electrical network simulation programs such as PSPICE.
This method is applied to the famous Brusselator system for a wide range of parameters. In the appendix the PSPICE program for some network model of Brusselator is given.
Reviewer: S.Burys (Kraków)

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
Software:
PSpice; SPICE
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