Finite difference discretization of the extended Fisher-Kolmogorov equation in two dimensions |
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| Authors: | Noomen Khiari Khaled Omrani |
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| Affiliation: | Institut Supérieur des Sciences Appliquées et de Technologie de Sousse, 4003 Sousse Ibn Khaldoun, Tunisia |
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| Abstract: | Approximate solutions are considered for the extended Fisher-Kolmogorov (EFK) equation in two space dimension with Dirichlet boundary conditions by a Crank-Nicolson type finite difference scheme. A priori bounds are proved using Lyapunov functional. Further, existence, uniqueness and convergence of difference solutions with order O(h2+k2) in the L∞-norm are proved. Numerical results are also given in order to check the properties of analytical solutions. |
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| Keywords: | Extended Fisher-Kolmogorov (EFK) equation Finite difference scheme Lyapunov functional Existence Uniqueness Convergence |
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