The network method for solutions of oscillating reaction-diffusion systems (Q1891107)

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.