EXPONENTIAL POLYNOMIAL BLOCK METHODS

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.

Automated summary

In this paper, exponential integration is introduced to initial value problems, resulting in a new class of parallel exponential polynomial block methods (EPBMs) with improved stability. High-order EPBMs are significantly more efficient than other methods in obtaining highly accurate solutions.