求解守恒型奇异摄动问题的一个一致收敛高阶方法

A Uniform High-Order Method for a Singular Perturbation Problem in Conservative Form

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.

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.