On the Stability Analysis of the Fisher Equation Based on Some Numerical Galerkin Techniques

Murat Ozcek

Gaziantep University, Department of Mathematics, Gaziantep, Turkey

muratozcek.12@gmail.com

Abstract

We studied the stability of the steady state solutions for Fisher Equation in two cases, the First one with constant amplitude and we show that the steady state solution  is always stable under any condition, but the other two solutions  and are conditionally stable.

In the Second case, we studied the steady state solutions for various amplitude by using two Methods. The First is analytically by direct Method and the second is numerical method using Galerkin technique which shows
the same results, that is the steady state solution  is always stable under any conditions, but the other two solutions  and  are conditionally stable.

Keywords: Galrekin techniques; Fisher's equation; Stability; Analysis; Numerical algorithm