Volume 3 • Issue 2 • PP: 12–16 • 2024
On the Stability Analysis of the Fisher Equation Based on Some Numerical Galerkin Techniques
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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We studied the stability of the steady-state solutions for the Fisher equation in two cases. In the first case, with constant amplitude, we show that the steady-state solution u1 = 1 is always stable under any condition, whereas the other two solutions, u1 = 0 and u1(x) = Acos(nπX), are conditionally stable. In the second case, we studied the steady-state solutions for variable amplitude using two methods. The first is an analytical direct method, and the second is a numerical method using the Galerkin technique. Both methods show the same results: the steady-state solution u1 = 1 is always stable under any conditions, whereas the other two solutions, u1 = 0 and u1(x) = Acos(nπX), are conditionally stable.
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