This paper presents a sequence of deferred correction (DC) schemes built recursively from the implicit midpoint scheme for the numerical solution of general first order ordinary differential equations (ODEs). It is proven that each scheme is A-stable, satisfies a B-convergence property, and that the correction on a scheme DC2j of order 2j of accuracy leads to a scheme DC2j + 2 of order 2j + 2. The order of accuracy is guaranteed by a deferred correction condition. Numerical experiments with standard stiff and non-stiff ODEs are performed with the DC2, ..., DC10 schemes. The results show a high accuracy of the method. The theoretical orders of accuracy are achieved together with a satisfactory stability.

本文提出了从隐式中点方案递归建立的一系列递推校正（DC）方案，用于一般一阶常微分方程（ODE）的数值解。证明每种方案都是A稳定的，满足B收敛性，并且对精度为2j的方案DC2j的校正导致方案为DC2j + 2为2j + 2的方案。保证了精度的顺序通过推迟的校正条件。使用DC2，...，DC10方案对标准的刚性和非刚性ODE进行了数值实验。结果表明该方法具有较高的准确性。达到了理论上的精度等级，并具有令人满意的稳定性。