Dissipativity of variable-stepsize Runge-Kutta methods for nonlinear functional differential equations with application to Nicholson’s blowflies models

Abstract

This paper deals with dissipativity of the variable-stepsize Runge-Kutta methods applied to nonlinear Volterra functional differential equations in Hilbert spaces. The conditional dissipativity of variable-stepsize Runge-Kutta methods is analyzed and hence some new numerical dissipative criteria are derived. The resulting dissipative criteria extend and improve the existing results. Especially, for the algebraically stable variable-stepsize Runge-Kutta methods, we obtain a sharper dissipative result. In the end, we apply some concrete variable-stepsize Runge-Kutta methods to the three classes of nonlinear Nicholson’s blowflies models. The presented numerical examples further illustrate the theoretical results.