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：我们提出将基本二阶格式与适当选取的系数进行组合的新的线性组合形式，以构造微分方程的高阶数值积分器。这些方法可视为外推方法和多乘积展开的推广。本文给出了通用分析框架，构建并测试了高达八阶的新方法。研究表明，新方法在并行环境中实现时可有效降低延迟问题，并且当线性组合延迟若干步时，所得到的格式比标准外推方法显著更高效。