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.

翻译：在本文中,我们扩展了多元时间整合框架,将分解和非分解初始值问题的指数集成纳入其中。然后,我们通过根据图例点建造新的一类平行的平行指数聚积块方法(EPBMs),展示了指数集成多边框架的有用性。这些新的集成器可以任意地按照准确性顺序构建,并且比现有的指数线性多步法更加稳定。此外,如果ODE右侧评价能够有效地平行进行,那么高等级的EPBMS在获得高度准确的解决方案方面比指数线性多步法和指数光谱延迟等同顺序的纠正方法效率要高得多。