Abstract
In this paper, a finite difference scheme is presented for the initial-boundary value problem for the two-dimensional nonlinear Fisher-Kolmogorov-Petrovski-Piskunov (Fisher-KPP) equation with mixed boundary conditions. Using Energy functional, stability of the suggested scheme is achieved. Unique solvability of the difference solutions is proved. Furthermore, the second-order convergence in the discrete H-1-norm is established. Finally, two numerical experiments are reported to validate the theoretical analysis.