二维变系数非齐次抛物型方程的紧交替方向差分格式

A Compact Alternate Direction Implicit Difference Method for the Two-dimension Parabolic Equations with Variable Coefficients

研究了二维变系数非齐次抛物型方程的紧交替方向隐式差分格式,首先运用算子方法导出了紧差分格式,给出了差分格式的截断误差,接着讨论了差分格式的稳定性和收敛性,最后给出了数值例子,数值结果和理论分析是吻合的。

This paper presents a compact high accuracy alternate direct implicit difference scheme for solving the two-dimensional parabolic equation with variable coefficients.Firstly,a compact difference scheme is derived by using operator method.Secondly,a compact ADI difference scheme is presented by introducing a variable of intermediate value.Thirdly,the stability and convergence of the ADI scheme are conducted by using Fourier method.Finally,a numercial example demonstrates the theoretical results.