Exploring Exponential Runge-Kutta Methods: A Survey
In this survey, we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems. These methods offer a valuable synthesis between classical Runge-Kutta methods, introduced more than a century ago, and exponential integrators, which date back to the 1960s. This manuscript presents both a historical analysis of the development of these methods up to the present day and several examples aimed at making the topic accessible to a broad audience.
Authors
- Alessia Andò (ORCID: https://orcid.org/0000-0002-4051-2049)
- Nicolò Cangiotti (ORCID: https://orcid.org/0000-0003-2200-446X)
- Mattia Sensi (ORCID: https://orcid.org/0000-0002-6631-0242)
Institutions
- University of Udine (IT)
- University of Trento (IT)
Publication Details
- Journal
- Communications in Mathematical Research
- Published
- 2026-04-16
- DOI
- https://doi.org/10.4208/cmr.2026-0024
- Primary Topic
- Numerical methods for differential equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
- Gruppo Nazionale per il Calcolo Scientifico