We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization of extrapolation methods and multi-product expansions. A general analysis is provided and new methods up to order 8 are built and tested. The new approach is shown to reduce the latency problem when implemented in a parallel environment and leads to schemes that are significantly more efficient than standard extrapolation when the linear combination is delayed by a number of steps.

翻译：我们提出新的线性组合方法，通过将基本二阶格式与适当选取的系数进行组合，构建微分方程的高阶数值积分器。这些方法可视为外推法和多乘积展开的推广。我们给出了通用分析框架，并构造并测试了高达8阶的新方法。研究表明，该新方法在并行环境下实现时能够降低延迟问题，并且当线性组合延迟若干步执行时，所得到的格式比标准外推法效率显著更高。