Numerical stability of brusselator system

Abstract EN

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 R1 ≤ (2-K (b+1) )/4, and r 2 ≤ 1 / 2.While the implicit method is unconditionally stable.

For two dimensional space we found that ADE method is stable under condition r1 ≤ (2-K (b+1))/8, and r < 1 / 4, while ADI is unconditionally stable.