A Stress Test for the Midpoint Time-Stepping Method

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Abstract

The midpoint method can be implemented as a sequence of Backward Euler and Forward Euler solves with half time steps, allowing for improved performance of existing solvers for PDEs. We highlight the advantages of this refactorization by considering some specifics of implementation, conservation, error estimation, adaptivity, stability, and performance on several test problems.

Keywords:

Midpoint method local error estimation time step adaptivity conservation B-stable.
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