Finite difference discretization of the extended FisherKolmogorov equation in two dimensions
Approximate solutions are considered for the extended FisherKolmogorov (EFK) equation in two space dimension with Dirichlet boundary conditions by a CrankNicolson 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 ( h 2 + k 2 ) in the L? L ? -norm are proved. Numerical results are also given in order to check the properties of analytical solutions.
extended fisherkolmogorov (efk) equation finite difference scheme lyapunov functional existence uniqueness convergence