Numerical Stability of Brusselator System

The numerical stability analysis of Brusselator system has been done in one and two dimensional space. For one dimension we studied the numerical stability for explicit and implicit (Crank- Nicolson) methods and we found that explicit method for solving Brusselator system is stable under the conditions , and
While the implicit method is unconditionally stable. For two dimensional space we found that ADE method is stable under condition , and , while ADI is unconditionally stable.