两点边值问题的一种高精度差分方法

从中心差分公式出发，利用二阶微分的四阶差分公式，对两点边值问题得到了一种四阶精度的差分格式，该方法仅涉及中心点及相邻网格点，具有四阶精度，并且由所提格式得到的线性方程组是三对角线型的，可以直接采用追赶法进行求解，数值算例的结果表明，该格式比以往的格式具有更高的精度，并且计算简便。

High-order finite difference method for solving two-points boundary value problem

Based on the fourth-order difference formula of the second derivative term,a fourth-order finite difference method is developed for solving two-points boundary value problem. Only center and neighboring points are used in present scheme, so the method of forward elimination and backward substitution can be directly used to solve linear simultaneous equations obtained from the scheme. Numerical tests show that the present scheme gives better results than that by existing ones.