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

摘要

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.