论文标题
指数多项式块方法
Exponential Polynomial Block Methods
论文作者
论文摘要
在本文中，我们将多项式时间集成框架扩展到包括分区和未分配初始值问题的指数集成。然后，我们通过基于Legendre点构建新的平行指数多项式块方法（EPBM）来证明指数多项式框架的实用性。与现有指数线性多步法方法相比，这些新的集成符可以以任意准确性的准确性顺序构建，并提高了稳定性。此外，如果可以有效地平行ODE右侧评估，则高阶EPBM在获得高度准确的解决方案方面比指数线性多步法方法和指数频谱递延校正方法明显更有效。
In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by constructing a new class of parallel exponential polynomial block methods (EPBMs) based on the Legendre points. These new integrators can be constructed at arbitrary orders of accuracy and have improved stability compared to existing exponential linear multistep methods. Moreover, if the ODE right-hand side evaluations can be parallelized efficiently, then high-order EPBMs are significantly more efficient at obtaining highly accurate solutions than exponential linear multistep methods and exponential spectral deferred correction methods of equivalent order.
