The diffusion-Brusselator equation

Aspects of a Distributed Solution of the Brusselator Equation

The spatial discretization of nonlinear partial differential equations (PDEs) results in large systems of nonlinear ordinary differential equations (ODEs). The discretization of the Brusselator equation is a characteristic example. For the parallel numerical solution of the Brusselator equation we use an iterated Runge-Kutta method. We propose modifications of the original method that exploit t...

Turing pattern formation in the Brusselator system with nonlinear diffusion.

In this work we investigate the effect of density-dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the pr...

Chapter 7 Two-Dimensional Reaction-Diffusion Brusselator System

Solutions of diffusion equation for point defects

An analytical solution of the equation describing diffusion of intrinsic point defects in semiconductor crystals has been obtained for a one-dimensional finite-length domain with the Robin-type boundary conditions. The distributions of point defects for different migration lengths of defects have been calculated. The exact analytical solution was used to verify the approximate numerical solutio...

Finite Element Methods for Convection Diffusion Equation

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...