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.

翻译：本综述深入研究了用于初值问题数值积分的指数龙格-库塔方法。这些方法在经典龙格-库塔方法（提出已逾百年）与指数积分器（可追溯至20世纪60年代）之间实现了有价值的融合。本文既呈现了该方法发展至今的历史分析，也提供了若干示例，旨在使广大读者能够理解这一主题。