Solving Numerical Solution of the Generalised Fisher Equation Using the Explicit Euler and the Crank-Nicholson Methods
DOI:
https://doi.org/10.54153/sjpas.2025.v7i4.1238Keywords:
Generalised Fisher equation, numerical solution, explicit method, Crank-Nicholson method, convergence analysis.Abstract
This study presents a numerical solution to the generalized Fisher equation (GFE) using two finite- difference numerical methods: the explicit method and the Crank-Nicholson method. The convergence for each method was analysed theoretically and experimentally, while examining the effect of the parameters δ on the system dynamics. The results showed that increasing δ leads to faster solution evolution and higher solution values. The explicit method was also computationally more efficient, while the Crank-Nicholson method outperformed the GFE in accuracy and stability. Using small time and spatial steps significantly improved the accuracy of the results. The results were validated through various numerical examples using MATLAB R2022a, confirming the effectiveness of both methods in modeling the complex phenomena described by the equation.
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