解多维抛物型方程的一族高精度的显式差分格式

A Class of High Accuracy Explicit Difference Scheme for Solving Parabolic Equations of Multi—Dimension

本文对N—维抛物型方程构造出一族含参数的高精度显格式，其截断误差阶达到O,并且稳定性条件是网格比且参数f 满足，其稳定性条件好于文[1]中的古典显式格式与文[2]中的显格式(当N≥3时)，其精度高于文[2]与文[3]中的显格式。它包含了文[4]中的差分格式。通过数值实例，表明了此格式是有效的。

In this paper, a class of explicit three-level difference schemes with parameters are derived for solving parabolic partial differential equation of N--dimension, and its local truncation error is of order. These Schemes is stable under he ondition ofand , (there of is parameter ,τ、h are time and space step length ), Its stable condition is better than that of Eulers explicit scheme in[l] and that of explicit scheme in[2] (n≥3) . Its accuracy is higher than that in[2] and in [3] .It includes difference scheme in[4].Finally, a numerical example shows that these schemes is effectives.