Editorial Board

JMI2011C-6 Application of the nonlinear Galerkin FEM method to the solution of the reaction diffusion equations (pp.41-51)

Author(s): Jan Mach

J. Math-for-Ind. 3C (2011) 41-51.

The article summarizes application of the nonlinear Galerkin method to the numerical solution of reaction-diffusion systems---the Gray-Scott model and simplified equation. The space discretization is performed by the finite-element method. For time integration we use the Runge- Kutta method with time step adaptivity. The computational results demonstrate properties of the method and the comparison with the finite difference method.

Keyword(s).  Nonlinear Galerkin method, Gray-Scott model, reaction-diffusion equation, method of lines, finite difference method, finite element method, Runge-Kutta-Merson method