Work

Exploring Exponential Runge-Kutta Methods: A Survey

Year: 2026

Type: article

Abstract: 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.

Source: Communications in Mathematical Research

DOI: 10.4208/cmr.2026-0024

Authors: Alessia Andò, Nicolò Cangiotti, Mattia Sensi

Institutions: University of Udine, Politecnico di Milano, University of Trento

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

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

Awards: G2528524749, G490430286, G597203450

OpenAlex ID: W4415345693

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