On one method of discretisation of the Fisher-Kolmogorov-Petrovsky-Piskunov problem

In this article, a two-layer six-point difference scheme with weights, which has the first order of approximation on the time variable and the second on the spatial variable, is studied for the quasilinear Fischer-Kolmogorov-Petrovsky-Piskunov equation. Using the maximum principle, an a priori estimate of the difference solution is obtained in the paper. The monotonicity of the difference scheme constructed with respect to the grid function, which is the difference between the solution of the difference problem with disturbed input data and the solution of the original difference problem, is proved. An estimate in the grid analogue of the norm C expressing the stability of the scheme with respect to a small disturbance of all input data is obtained. The results of numerical experiment are given.