Discretized Stability and Error Growth of The Nonautonomous Pantograph Equation

Authors:
Chengming Huang;Stefan Vandewalle
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2004

Citing 0
Cited 3

Recent advances in the numerical analysis of Volterra functional differential equations with variable delays

Journal of Computational and Applied Mathematics
High Order Contractive Runge-Kutta Methods for Volterra Functional Differential Equations

SIAM Journal on Numerical Analysis
Asymptotic stability of Rosenbrock methods for systems of functional differential and functional equations

Mathematical and Computer Modelling: An International Journal

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Abstract

This paper is concerned with the stability properties of Runge--Kutta methods for the pantograph equation, a functional differential equation with a proportional delay. The focus is on nonautonomous equations. Both linear and nonlinear cases are considered. Sufficient and necessary conditions for the asymptotic stability of the numerical solution of general neutral pantograph equations are given. An upper bound for the error growth is investigated for algebraically stable methods applied to nonneutral equations. Finally, some stability results are extended to the case of a more general class of equations.