Neutrosophic and Information Fusion NIF 2836-7863 10.54216/NIF https://www.americaspg.com/journals/show/3058 2023 2023 Gaziantep University, Department of Mathematics, Gaziantep, Turkey Murat Murat 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 u1=1 is always stable under any condition, but the other two solutions u1=0 and u1 (x)=A cos (nπX)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 u1=1 is always stable under any conditions, but the other two solutions u1=0 and u1 (x)=A cos (nπX) are conditionally stable. 2024 2024 18 24 10.54216/NIF.030203 https://www.americaspg.com/articleinfo/39/show/3058