Explicit exponential Runge–Kutta methods for semilinear parabolic delay differential equations

Abstract

This paper is concerned with explicit exponential Runge–Kutta methods for semilinear parabolic delay differential equations. Stiff convergence and conditional DN-stability of explicit exponential Runge–Kutta methods are investigated in the framework of analytic semigroup on a Banach space. We derive the stiff convergence order conditions up to order four. In particular, it is shown that explicit exponential Runge–Kutta methods are conditionally DN-stable. Finally, numerical experiments are presented to validate the convergence results.