On the L∞-norm convergence of a three-level linearly implicit finite difference method for the extended Fisher-Kolmogorov equation in both 1D and 2D

In this paper, we propose a second-order three-level linearly implicit finite difference method for solving the extended Fisher-Kolmogorov equation in both 1D and 2D. The existence and uniqueness of the proposed scheme is proved, the stability and convergence of numerical solution in L ∞ -norm are established. The proposed linear method is generally much more efficient than the existing nonlinear methods.

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