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 its utility by constructing a new class of parallel exponential block methods based on the Legendre points. These new integrators can be constructed at arbitrary orders of accuracy , have improved stability compared to existing polynomial based exponential linear multistep methods , and can offer significant computational savings compared to current state-of-the-art 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 .
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its utility
the utility of the exponential polynomial framework
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block methods
polynomial block methods (EPBMs)
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polynomial based
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, and can offer significant computational savings compared to current state-of-the-art 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