本文首次推导出了变步长的Hermite差分公式,用它来计算变截面柱的临界荷载,这是一个很有效的新的数值方法。Hermite差分法的特点是:它所构造的差分格式中不仅含有未知位移函数在网格点上的值,而且还包含未知函数的导数在这些点上的值。因而它与有限差分法相比较,在相同的网格情况下可以提高精度,通过算例说明,该方法的优越性是明显的。 In this paper, the Hermite difference formula with variable step size is deduced for the first time. It is used to calculate the critical load of variable column. This is a very effective new numerical method. The Hermite difference method is characterized in that the differential format it constructs contains not only the value of the unknown displacement function at the grid point, but also the value of the derivative of the unknown function at these points. Therefore, compared with the finite difference method, it can improve the accuracy under the same grid condition. The example shows that the superiority of this method is obvious.