Exponential Runge-Kutta methods for delay equations in the sun-star abstract framework

Exponential Runge-Kutta methods for semi-linear 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 motivated the present work. The result was a general approach that allowed us to define the methods explicitly and analyze their convergence properties in a unifying way.