An explicit positivity-preserving finite-difference scheme for the classical Fisher–Kolmogorov–Petrovsky–Piscounov equation

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In this work, we introduce a family of explicit finite-difference schemes to approximate positive solutions of the classical Fisher–Kolmogorov–Petrovsky–Piscounov equation from population dynamics. A Neumann stability analysis reveals that our methods are indeed stable under certain choices of the model and numerical parameters, and numerical comparisons with analytical solutions are carried out in some detail.