In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(Δt 4+Δx 4) It can be easily solved by double sweeping method.
A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2<1/2 and the truncation err or is O(Δt 3+Δx 4).
This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△x4). The stability condition is r=a△t/△x2<1/2.
