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This analysis demonstrates improved accuracy in solving Fisher-Kolmogorov equations using advanced numerical methods, suggesting better modeling of nonlinear phenomena.
This article analyzes hybrid high-order method for space discretization and backward Euler and Crank- Nicolson schemes for time discretization of the nonlinear extended Fisher-Kolmogorov and the Fisher- Kolmogorov equations. The critical parameter γ > 0 is incorporated in the stabilization term of the HHO method. The HHO discretization for the Fisher-Kolmogorov equation, that is, when the parameter γ = 0, leads to a convergence rate of O(h^(k+2)) in the space variable. The results of the numerical experiments validate the theoretical results.
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Nataraj et al. (2026) studied this question.
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