Multirate finite step methods with varying step sizes

Multirate finite step methods with varying step sizes Many partial differential equations consist of slow and fast scales. Often, the right hand side of semidiscretized PDEs can be split additively in corresponding fast and slow parts. Many methods utilise the additive splitting of these equations, like generalized additive Runge‐Kutta (GARK) methods or multirate infinitesimal step methods. The latter one treat the slow part with macro step sizes, whereas the fast part is integrated a ODE solver. The corresponding order conditions assume the exact solution of the auxiliary ODE, i.e. assume an infinite number of small steps. We extend the MIS approach by fixing the number of steps, which leads to the multirate finite steps (MFS) method. The order conditions are derived, such that the order is independent in the number of small steps in each stage. Finally, we confirm the theoretical results by numerical experiments. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

Multirate finite step methods with varying step sizes

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710393
Publisher site
See Article on Publisher Site

Abstract

Many partial differential equations consist of slow and fast scales. Often, the right hand side of semidiscretized PDEs can be split additively in corresponding fast and slow parts. Many methods utilise the additive splitting of these equations, like generalized additive Runge‐Kutta (GARK) methods or multirate infinitesimal step methods. The latter one treat the slow part with macro step sizes, whereas the fast part is integrated a ODE solver. The corresponding order conditions assume the exact solution of the auxiliary ODE, i.e. assume an infinite number of small steps. We extend the MIS approach by fixing the number of steps, which leads to the multirate finite steps (MFS) method. The order conditions are derived, such that the order is independent in the number of small steps in each stage. Finally, we confirm the theoretical results by numerical experiments. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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