Exponential Runge-Kutta methods for semilinear ordinary differential equations can be extended to abstract differential equations, defined on Banach spaces. Thanks to the sun-star theory, both delay differential equations and renewal equations can be recast as abstract differential equations, which motivates the present work. The result is a general approach that allows us to define the methods explicitly and analyze their convergence properties in a unifying way.

翻译：指数Runge-Kutta方法可推广至定义在巴拿赫空间上的抽象微分方程，以求解半线性常微分方程。借助太阳-星理论，时滞微分方程与更新方程均可重构为抽象微分方程，这构成了本研究的动机。由此形成了一种通用方法，使我们能够明确定义这些方法，并以统一的方式分析其收敛性质。