Abstract: This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equa-tion (2.1) is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite dif-ference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.

Key words: reaction-diffusion equation, difference scheme, stability problem, incremental
unknowns