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

• Published in: Applied numerical mathematics Vol. 37; no. 1; pp. 161 - 170
• Main Authors: Zhang, C.J., Zhou, S.Z., Liao, X.X.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.04.2001; Elsevier
• Subjects: Exact sciences and technology; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Sciences and techniques of general use; Lagrangian; Stability; Existence theorem; Error estimation; Differential equation; Delay system; Jacobi matrix; Runge Kutta method; Delay equation; Convergence; Interpolation; Analysis method; Lagrange interpolation; Lagrangian method; Taylor formula

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 tha...