【摘要】 <正> 本文考虑如下的高阶（2m阶）抛物型方程周期初值问题 φu/φt=（-1）^m+1φ^2mu/φx^2m（-∞<x<∞,0≤t≤T） u（x+L,t）=u（x,t）（-∞<x<∞,0≤t≤T） （1） u（x,0）=f（x） （-∞<x<∞）更多还原

【Abstract】 A family of three-layer implicit difference Schemes of high accuracy with two parameters for solving high order parabolic equation (where m is positive integers) are constructed. 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 arbiratily chosen non-negative parameters, And the order of the truncation error is O((Δt)2 +(Δx)6). They are shown by numerical examples to be effective, and practice consistant with theoretical analysis.更多还原