A family of three-layer implicit difference schemes of high accuracy with two parameters for solving high order Schroedinger type equation au/at = i(-1)^m a^2mu/ax^2m are constructed(where i = √-1,m is positive integers). In the special case α =1/2,β = 0,we obtain a two-layer difference scheme. These schemes are proved to be absolutely stable for arbitrarily chosen non-negative parameters, and the order of the truncation error is O((△t)^2 + (△x)^4). They are shown by numerical examples to be effective, and practice consistant with theoretical analysis.
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