On the L∞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∞L∞-norm are established. The proposed linear method is generally much more efficient than the existing nonlinear methods.