Abstract: Solutions to the initial boundary value problem with onedimension parabolic equations were presented. On the basis of mesh，an implicit difference scheme with multiple variables was given by the undetermined parameters method. Then, it was expanded with Taylor series by combining the characteristics of partition differential equations in x_j、t_n, to reach certain accuracy. Finally, parameters of the equation were determined. Via this method, an implicit difference scheme of two layers and eight points for solving parabolic equation was constructed. The order of truncation error was O(τ³+h⁵), and the stability condition was 0.001<r<0.231 or 0.236<r<0.772. The corresponding numerical example has been given to demonstrate the feasibility and effectiveness of the proposed method.

Key words: one-dimension parabolic equation; implicit difference scheme; order of truncation error; stability condition