Exploring Exponential Runge-Kutta Methods: A Survey
It synthesizes classical and exponential methods for researchers in numerical analysis, but is incremental as a survey.
This survey investigates exponential Runge-Kutta methods for numerical integration of initial-value problems, providing a historical analysis and examples to make the topic accessible.
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.