泊松方程的高精度三次样条差分方法

Cubic-spline difference method of high accuracy for Poisson equation

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.