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.
翻译:在这项工作中,我们提出了一套新颖的可平行的高顺序时间整合计划,以大致解决添加式脱氧核糖核酸。这些方法通过结合一种适当的四方公式实现高顺序,该方公式涉及极右侧的多种衍生物和一个预测者-纠正者-安萨兹。后一种方法的设计方式是,能够及时实现平行。我们提出了透彻的分析以及数字结果,展示了从这一类解答者那里推广方法的机会。