Stability and convergence of Runge-Kutta methods for nonlinear neutral functional differential equations

Abstract

This paper concerns the stability and convergence of Runge-Kutta methods for nonlinear neutral functional differential equations (NFDEs). Based on the B-theory of Runge-Kutta methods for Volterra functional differential equations (VFDEs), we introduce the concepts of EB-stability and EB-convergence of Runge-Kutta methods for NFDEs and obtain EB-stability and EB-convergence results on variable stepsize Runge-Kutta methods for this class of equations. These results are new even for neutral delay differential equations and neutral delay integro-differential equations.