二维变系数抛物型方程高精度恒稳定的改进的Douglas格式

An Improved Douglas Scheme with Absolute Stability and High Accuracy for 2-D Varying Coefficient Parabolic Equation

本文将算子方法和粘结系数方法相结合,构造出了求二维变系数抛物型方程的改进的Douglas格式,格式的截断误差阶达O(τ2+h4),并用Fourier分析方法讨论了格式的绝对稳定性.文末给出的数值例子表明了本文理论分析的正确性和所构造格式的有效性及优越性.长期以来,现有关于抛物型方程的差分格式都是对常系数方程而言的,本文较简便的给出了二维情形下变系数抛物型方程的差分解法,此方法完全可以推广到高维情形.

This paper presents an improved Douglas scheme with absolute stability and high accuracy for solving 2-D varying coefficient parabolic equation. The truncation error of the proposed scheme is O（τ^2＋h^4）. The effectiveness and advantages of the proposed scheme is substantiated by a numerical example. Furthermore, this scheme can be easily extended to high dimensional cases.