Numerical Solutions and Stability Analysis of Brusselator System

In this work we studied the numerical solution of the Brusselator model in one dimension using FDM including explicit and implicit methods; FEM with weighted residual methods and iterative methods. Also we studied the numerical solution of the Brusselator model in two dimensions using ADI ( Alternating Direction Implicit) and ADE (Alternating Direction Explicit) methods. Besides we studied the numerical stability of FDM (explicit and implicit methods); the numerical stability analysis of the Brusselator system was done in one-dimensional space and two-dimensional spaces. For one dimensional space we have studied the numerical stability for explicit and implicit (Crank- Nicolson) methods and we have found the stability condition for explicit method whereas the implicit method is unconditionally stable. For two dimensional space we found the stability condition for ADE method while ADI is unconditionally stable.