D-convergence and GDN-stability of Runge–Kutta methods for a class of delay systems Original Research Article

This paper deals with convergence and stability analysis of Runge–Kutta methods with the Lagrangian interpolation (RKLMs) for a class of delay systems. We show that DA-, DAS- and ASI-stability of the Runge–Kutta methods (RKMs) for ODEs imply GDN-stability of the corresponding RKLMs for DDEs, and that a DA-, DAS- and ASI-stable RKM with stage order p, together with a Lagrangian interpolation of order q, results in a D-convergent RKLM of order View the MathML source.