This paper deals with the stability analysis of numerical methods for the solution of advanced differential equations with piecewise continuous arguments. We focus on the behaviour of the one-leg 0-method and the linear 0-method in the solution of the equation x'(t) = ax(t)+aox([t])+ alx([t+ 1]), with real a, a0, al and [.] designates the greatest-integer function. The stability regions of two 0-methods are determined. The conditions under which the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given. (~)
In this paper, the asymptotical stability of the analytic solution and the numerical methods with constant stepsize for pantograph equations is investigated using the Razumikhin technique. In particular, the linear pantograph equations with constant coefficients and variable coefficients are considered. The stability conditions of the analytic solutions of those equations and the numerical solutions of the θ-methods with constant stepsize are obtained. As a result Z. Jackiewicz's conjecture is partially proved. Finally, some experiments are given. (2000): 65L02, 65L05, 65L20.
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