High order explicit exponential Runge–Kutta methods for semilinear delay differential equations

Abstract

This paper aims to analyze order conditions of high order explicit exponential Runge–Kutta methods for stiff semilinear delay differential equations. Under the framework of analytic semigroup and the natural assumptions on the delay differential equations, the stiff order conditions up to order five are derived. Further, we show the method is stiffly convergent of order p even if the order conditions of order p holding in a weak form. Numerical tests are carried out to demonstrate the superiority of high order methods.