Maset, S.; Zennaro, M. Stability properties of explicit exponential Runge-Kutta methods. (English) Zbl 1271.65117 IMA J. Numer. Anal. 33, No. 1, 111-135 (2013). The authors deal with the stability properties of exponential Runge-Kutta methods, when applied to ordinary differential equations with a stiff linear part and a nonstiff nonlinear part. Equations of that type, e.g., arise after a space discretization of parabolic partial differential equations. Here the focus of the authors is on the analysis of explicit exponential Runge-Kutta schemes. The stability properties of the exponential Runge-Kutta methods are derived from their application to a an appropriate linear test-equation. Necessary conditions to ensure unconditional and conditional stability of explicit methods are presented. Finally, the existing numerical schemes are classified and some numerical applications are presented. Reviewer: Johannes Schropp (Konstanz) Cited in 9 Documents MSC: 65L20 Stability and convergence of numerical methods for ordinary differential equations 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 65L04 Numerical methods for stiff equations Keywords:initial value problems; exponential Runge-Kutta methods; stability; numerical examples; stiff linear part; nonstiff linear part Citations:Zbl 1198.65127 PDFBibTeX XMLCite \textit{S. Maset} and \textit{M. Zennaro}, IMA J. Numer. Anal. 33, No. 1, 111--135 (2013; Zbl 1271.65117) Full Text: DOI