解三维抛物型方程的一个ADI格式

An ADI scheme for solving parabolic equation of three-dimension

构造了一个解三维抛物型方程的高精度ADI格式,格式绝对稳定,截断误差为O(△t2+△x4);然后应用Richerdson外推法,外推一次得到了具有O(△t3+△x6)阶精度的近似解.

This paper presents an ADI scheme of high accuracy for solving parabolic equation of threedimension. 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.