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arXiv · 2507.04024

Exploring Exponential Runge-Kutta Methods: A Survey

Alessia andò·Nicolò Cangiotti·Mattia Sensi
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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.

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Alessia andò, Nicolò Cangiotti, Mattia Sensi. 2026-02-11. Exploring Exponential Runge-Kutta Methods: A Survey. https://doi.org/10.4208/cmr.2026-0024

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