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Unconditional stability of explicit exponential Runge-Kutta methods for semi-linear ordinary differential equations
Author(s):
S.
Maset;
M.
Zennaro.
Journal:
Math. Comp.
78
(2009),
957-967.
MSC (2000):
Primary 65L20
Posted:
August 18, 2008
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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:
10.1090/S0025-5718-08-02171-6
PII:
S 0025-5718(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
Posted:
August 18, 2008
Additional Notes:
This work was supported by the Italian MIUR and INdAM-GNCS.
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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