三维抛物型方程的一个高精度恒稳定的PC格式

A PC scheme of high accuracy with absolutely stable for solving parabolic equation of three-dimension

对三维抛物型方程,构造了一个高精度恒稳定的PC格式,格式的截断误差阶达到O(△t2+△x4),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二位以上有效数字;然后将Richardson外推法应用于本文格式,得到了具有O(△t3+△x6)阶精度的近似解,并将所得格式推广到了四维情形.

This paper presents a PC scheme of high accuracy for solving parabolic equation of three-dimension. The scheme is absolutely stable and the truncation error for the method is O（△t^2 ＋ △x^4）; Then Richardson＇s extrapolation method is successfully applied to the scheme and the approximate solution with accuracy O（△t^3 ＋ △x^6） is gained with once extrapolation. Finally, the scheme is generalized to solve parabolic equation of fourdimention.