Finite difference discretization of the extended Fisher–Kolmogorov equation in two dimensions

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)O(h2+k2) in the L∞L∞-norm are proved. Numerical results are also given in order to check the properties of analytical solutions.