{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:42:55Z","timestamp":1776789775755,"version":"3.51.2"},"reference-count":26,"publisher":"American Mathematical Society (AMS)","issue":"266","license":[{"start":{"date-parts":[[2009,8,18]],"date-time":"2009-08-18T00:00:00Z","timestamp":1250553600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>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.<\/p>","DOI":"10.1090\/s0025-5718-08-02171-6","type":"journal-article","created":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T13:09:23Z","timestamp":1259672963000},"page":"957-967","source":"Crossref","is-referenced-by-count":33,"title":["Unconditional stability of explicit exponential Runge-Kutta methods for semi-linear ordinary differential equations"],"prefix":"10.1090","volume":"78","author":[{"given":"S.","family":"Maset","sequence":"first","affiliation":[]},{"given":"M.","family":"Zennaro","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2008,8,18]]},"reference":[{"issue":"2-3","key":"1","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/S0168-9274(97)00056-1","article-title":"Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations","volume":"25","author":"Ascher, Uri M.","year":"1997","journal-title":"Appl. Numer. 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