Deferred correction is a well-established method for incrementally increasing the order of accuracy of a numerical solution to a set of ordinary differential equations. Because implementations of deferred corrections can be pipelined, multi-core computing has increased the importance of deferred correction methods in practice, especially in the context of solving initial-value problems. In this paper, we review the theoretical underpinnings of deferred correction methods in a unified manner, specifically the classical algorithm of Zadunaisky/Stetter, the method of Dutt, Greengard and Rokhlin, spectral deferred correction, and integral deferred correction. We highlight some nuances of their implementations, including the choice of quadrature nodes, interpolants, and combinations of discretization methods, in a unified notation. We analyze how time-integration methods based on deferred correction can be effective solvers on modern computer architectures and demonstrate their performance. Lightweight and flexible Matlab software is provided for exploration with modern variants of deferred correction methods.

递延校正是一种行之有效的方法，用于逐步提高一组常微分方程数值解的精度。由于延迟校正的实现方式可以流水线化，因此多核计算在实践中尤其是在解决初值问题的背景下，增加了延迟校正方法的重要性。在本文中，我们以统一的方式回顾了延迟校正方法的理论基础，特别是Zadunaisky / Stetter的经典算法，Dutt，Greengard和Rokhlin的方法，频谱延迟校正和积分延迟校正。我们以统一的符号强调了其实现的一些细微差别，包括选择正交节点，内插值以及离散化方法的组合。我们分析了基于延迟校正的时间积分方法如何成为现代计算机体系结构上的有效求解器，并展示了它们的性能。提供了轻巧灵活的Matlab软件，用于探究延期校正方法的现代变体。