On the lack of convergence of unconditionally stable explicit rational runge-kutta schemes

A. Peirce; J. H. Prevost

doi:10.1016/0045-7825(86)90011-3

On the lack of convergence of unconditionally stable explicit rational runge-kutta schemes

A. Peirce, J. H. Prevost

Civil & Environmental Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

The poor performance of the rational Runge-Kutta (RRK) schemes of Hairer [2,3] are investigated. By considering two simple model problems, it is demonstrated that this poor performance is in fact due to a lack of convergence. A conceptual model of an unconditionally stable implicit-explicit time-integration scheme is also considered. With the aid of this model, it is possible to establish necessary bounds on the extent of the explicit region for convergence. This demonstrates the limited applicability of such hybrid time-integration schemes.

Original language	English (US)
Pages (from-to)	171-180
Number of pages	10
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	57
Issue number	2
DOIs	https://doi.org/10.1016/0045-7825(86)90011-3
State	Published - Aug 1986

All Science Journal Classification (ASJC) codes

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/0045-7825(86)90011-3

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title = "On the lack of convergence of unconditionally stable explicit rational runge-kutta schemes",

abstract = "The poor performance of the rational Runge-Kutta (RRK) schemes of Hairer [2,3] are investigated. By considering two simple model problems, it is demonstrated that this poor performance is in fact due to a lack of convergence. A conceptual model of an unconditionally stable implicit-explicit time-integration scheme is also considered. With the aid of this model, it is possible to establish necessary bounds on the extent of the explicit region for convergence. This demonstrates the limited applicability of such hybrid time-integration schemes.",

author = "A. Peirce and Prevost, {J. H.}",

note = "Funding Information: The authors wish to thank Prof. R. Vichnevetskyf or helpful discussionsa nd Sara J. Lacy for carrying out the numerical experiments.T he first author was supported by the CSIR of South Africa and the Fulb~ght Foundation. This support is most gratefully acknowledged. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",

year = "1986",

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doi = "10.1016/0045-7825(86)90011-3",

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AU - Peirce, A.

AU - Prevost, J. H.

N1 - Funding Information: The authors wish to thank Prof. R. Vichnevetskyf or helpful discussionsa nd Sara J. Lacy for carrying out the numerical experiments.T he first author was supported by the CSIR of South Africa and the Fulb~ght Foundation. This support is most gratefully acknowledged. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1986/8

Y1 - 1986/8

N2 - The poor performance of the rational Runge-Kutta (RRK) schemes of Hairer [2,3] are investigated. By considering two simple model problems, it is demonstrated that this poor performance is in fact due to a lack of convergence. A conceptual model of an unconditionally stable implicit-explicit time-integration scheme is also considered. With the aid of this model, it is possible to establish necessary bounds on the extent of the explicit region for convergence. This demonstrates the limited applicability of such hybrid time-integration schemes.

AB - The poor performance of the rational Runge-Kutta (RRK) schemes of Hairer [2,3] are investigated. By considering two simple model problems, it is demonstrated that this poor performance is in fact due to a lack of convergence. A conceptual model of an unconditionally stable implicit-explicit time-integration scheme is also considered. With the aid of this model, it is possible to establish necessary bounds on the extent of the explicit region for convergence. This demonstrates the limited applicability of such hybrid time-integration schemes.

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On the lack of convergence of unconditionally stable explicit rational runge-kutta schemes

Abstract

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