一种基于紧致差分算子的扩散方程离散格式构造及分析

Construction and Analysis for Discrete Scheme of The Diffusion Equation based on Compact Difference Operator

针对扩散方程,构造了方程的离散格式.首先,时间方向上采用有限差分法进行离散,空间方向上引入了一个紧致差分算子,从而构建出扩散方程的离散格式.其次,证明了此离散格式是无条件稳定的,并给出了误差估计,其误差的收敛阶为O(τ^(2)+h^(4)),其中,τ和h分别为时间和空间步长.

For diffusion equation,the discrete scheme of the equation was constructed.First,the finite difference method was used in time direction and the compact difference operator was used in space direction.Secondly,we show that the dwascrete scheme was unconditionally stable and the error estimate are given.The convergence order was O(τ^(2)+h^(4)),whereτand this the temporal and spatial step sizes,respectively.