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Zbl 1198.65127
Maset, S.; Zennaro, M.
Unconditional stability of explicit exponential Runge-Kutta methods for semi-linear ordinary differential equations. (English)
[J] Math. Comput. 78, No. 266, 957-967 (2009). ISSN 0025-5718; ISSN 1088-6842/e

Summary: 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.

MSC 2000:: *65L20 Stability of numerical methods for ODE
65L06 Multistep, Runge-Kutta, and extrapolation methods

Keywords: ordinary differential equations; initial value problems; exponential Runge-Kutta methods; stability analysis

Cited in: Zbl pre06139389

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Zentralblatt MATH Berlin [Germany]