【摘要】 本文对守型恒奇异摄动问题（1.1）给出了一个一致收敛的高阶方法.首先将原问题（1.1）转换为二个一阶初值问题（1.4）,即（1.1）的解是（1.4）的两个解的线性组合.然后对初值问题（1.4）构造了一个O(h^m+1)一致收敛的差分格式.因此由关系式（1.3）,我们得到了原问题的一个O(h^m+1)一致精度的解,这里m是任意给定的非负整数.最后给出了数值结果.更多还原

【Abstract】 A uniform high-order method is presented for the numerical solution of a singular perturbation problem in conservative form.We first replace the original second-order problem (1.1) by two equivalent first-order problems (1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O(hm+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O(hm+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.更多还原