首先讨论了隐差分解与显差分解的关系，并利用差分解的渐近展开式构造差分校正解来提高精度。

The relation between the explicit difference solution and the implicit one is established. A correction difference solution with higher accuracy is constructed by the use of asymptotic expansion.

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基于中间点的渐近性质，获得了数值积分的校正公式及其条件误差估计。

Then Based on the asymptotic properties of the intermediate point, corrective formulas of numerical integral and its conditional errors are obtained.

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我们利用边界层校正法以及微分不等式理论证明了解的存在定理，并构造出其解的一致有效渐近展开式。

Using the method of boundary layer correction and the differential inequality theory, we prove the existence theorem of solutions and construct the uniformly valid asymptotic expansions of.

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