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

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...

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Published inApplied numerical mathematics Vol. 37; no. 1; pp. 161 - 170
Main Authors Zhang, C.J., Zhou, S.Z., Liao, X.X.
Format Journal Article
LanguageEnglish
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
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Summary: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 min{p,q+1} .
ISSN:0168-9274
1873-5460
DOI:10.1016/S0168-9274(00)00032-5