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Unconditional stability of explicit exponential Runge-Kutta methods for semi-linear ordinary differential equations


Authors: S. Maset and M. Zennaro
Journal: Math. Comp. 78 (2009), 957-967
MSC (2000): Primary 65L20
DOI: https://doi.org/10.1090/S0025-5718-08-02171-6
Published electronically: August 18, 2008
MathSciNet review: 2476566
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Abstract: In this paper we define unconditional stability properties of exponential Runge-Kutta methods when they are applied to semi-linear systems of ordinary differential equations characterized by a stiff linear part and a non-stiff non-linear part. These properties are related to a class of systems and to a specific norm. We give sufficient conditions in order that an explicit method satisfies such properties. On the basis of such conditions we analyze some of the popular methods.


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Additional Information

S. Maset
Affiliation: Dipartimento di Matematica e Informatica, Università di Trieste, Trieste, Italy

M. Zennaro
Affiliation: Dipartimento di Matematica e Informatica, Università di Trieste, Trieste, Italy

DOI: https://doi.org/10.1090/S0025-5718-08-02171-6
Keywords: Ordinary differential equations, initial value problems, exponential Runge-Kutta methods, stability analysis.
Received by editor(s): October 25, 2006
Received by editor(s) in revised form: April 14, 2008
Published electronically: August 18, 2008
Additional Notes: This work was supported by the Italian MIUR and INdAM-GNCS.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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