Abstract: The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability of the scheme. Through the stability analyzing for the scheme, it was shown that the stability of the finite difference scheme with the incremental unknowns is improved when compared with the stability of the corresponding classic difference scheme.

Key words: finite difference, partial differential equation, stability research, incremental
unknowns