高维抛物型方程的高精度恒稳定的改进的Douglas格式

An Absolutely Stable Improved Douglas Scheme of High Accuracyfor Solving Parobolic Equation

对二维和三维抛物型方程,构造出了高精度恒稳定的改进的Douglas格式,格式的截断误差阶达到O(Δt2+Δx4),通过数值实例,验证了所得格式较现有的同类格式的精度提高了2位以上有效数字.

This paper presents the absolutely stable improved Douglas scheme of high accuracy of solving parabolic equation of two-dimension and three-dimension.The truncation error of the scheme is O（Δt2＋Δx4）.From numerical examples,it validities that the accuracy of the scheme gained is hightened more than two effective numbers than the same existing style.