Exploring Exponential Runge-Kutta Methods: A Survey
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.
Fields of Study & Subjects
Numerical methods for differential equations
Model Reduction and Neural Networks
Publication details
- Journal / source
- Communications in Mathematical Research
- Volume
- 42
- Issue
- 2
- Pages
- 191–240
- Publication date
- 16 April 2026