article

Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs

Authors:

M. TokmanAuthors Info & Claims

Journal of Computational and Applied Mathematics, Volume 241

Pages 45 - 67

https://doi.org/10.1016/j.cam.2012.09.038

Published: 01 March 2013 Publication History

Abstract

Exponential integrators have enjoyed a resurgence of interest in recent years, but there is still limited understanding of how their performance compares with that of state-of-the-art integrators, most notably the commonly used Newton-Krylov implicit methods. In this paper we present comparative performance analysis of Krylov-based exponential, implicit and explicit integrators on a suite of stiff test problems and demonstrate that exponential integrators have computational advantages compared to the other methods, particularly as problems become larger and more stiff. We argue that the faster convergence of the Krylov iteration within exponential integrators accounts for the main proportion of the computational savings that they provide and illustrate how the structure of these methods ensures such efficiency. In addition, we demonstrate the computational advantages of the newly introduced Tokman and Loffeld (2010) [17] exponential propagation Runge-Kutta (EpiRK) fifth-order methods. The detailed analysis of the performance of the methods that is presented provides guidelines for the construction and implementation of efficient exponential methods and the quantitative comparisons inform the selection of appropriate schemes for other problems.

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cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 241, Issue

March, 2013

142 pages

ISSN:0377-0427

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Copyright © Elsevier B.V. © 2012.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 March 2013

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Cited By

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Naranjo-Noda FJimenez J(2024)Jacobian-free Locally Linearized Runge–Kutta method of Dormand and Prince for large systems of differential equationsJournal of Computational and Applied Mathematics10.1016/j.cam.2024.115974449:COnline publication date: 15-Oct-2024
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Gaudreault SCharron MDallerit VTokman M(2022)High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere gridJournal of Computational Physics10.1016/j.jcp.2021.110792449:COnline publication date: 15-Jan-2022
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Narayanamurthi MSandu A(2020)Efficient implementation of partitioned stiff exponential Runge-Kutta methodsApplied Numerical Mathematics10.1016/j.apnum.2020.01.010152:C(141-158)Online publication date: 1-Jun-2020
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