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TW 352

C. Huang, S. Vandewalle
Discretized stability and error growth of the non-autonomous pantograph equation

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 non-autonomous 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 also investigated for algebraically stable methods applied to nonneutral equations.