摘要
给出一种求解泊松方程的新数值方法:以二维泊松方程为例,首先将其转化成一维方程,然后将根据由三次样条插值公式导出的四阶精度三次样条差分公式,应用到一维方程之中,最终建立起二维泊松方程矩形网格下九结点差分格式,并给出了误差估计和数值结果。
A new finite difference (FD) method using nine grid points is presented for solving two-dimensional (2D) Poisson equation. First, 2D equation is transfered to 1D equation. Then, 1D equation is discerted by utilizing 3-spline difference formula inducing four order accuracy. Finally, we obtain a difference scheme which has four order accuracy for rectangular cells with an arbitrary length-to-width ratio. Numerical example is given to illustrate the present method.
出处
《西北师范大学学报(自然科学版)》
CAS
1996年第2期13-17,共5页
Journal of Northwest Normal University(Natural Science)
关键词
泊松方程
精度
三次样条
差分方法
边值问题
Poisson equation
higher accuracy
cubic-spline
difference method