In this work, we present a novel class of parallelizable high-order time integration schemes for the approximate solution of additive ODEs. The methods achieve high order through a combination of a suitable quadrature formula involving multiple derivatives of the ODE's right-hand side and a predictor-corrector ansatz. The latter approach is designed in such a way that parallelism in time is made possible. We present thorough analysis as well as numerical results that showcase scaling opportunities of methods from this class of solvers.

中文翻译：

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实时高阶多导数IMEX求解器

在这项工作中，我们提出了一类新的可并行化的高阶时间积分方案，用于加法ODE的近似解。该方法通过将包含ODE右手边的多个导数和预测器-校正器ansatz的合适正交公式相结合来实现高阶。后一种方法的设计方式使时间并行成为可能。我们提供详尽的分析以及数值结果，这些结果展示了此类求解器中方法的扩展机会。