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

Maset, S.; Zennaro, M.

doi:10.1090/S0025-5718-08-02171-6

Unconditional stability of explicit exponential Runge-Kutta methods for semi-linear ordinary differential equations
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by S. Maset and M. Zennaro;

Math. Comp. 78 (2009), 957-967

DOI: https://doi.org/10.1090/S0025-5718-08-02171-6

Published electronically: 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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Mathematics of Computation

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