Numerical analysis for the two-dimensional Fisher–Kolmogorov–Petrovski–Piskunov equation with mixed boundary condition.

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. [ABSTRACT FROM AUTHOR]