Journal
BIT NUMERICAL MATHEMATICS
Volume 45, Issue 4, Pages 743-759Publisher
SPRINGER
DOI: 10.1007/s10543-005-0022-3
Keywords
pantograph equation; Razumikhin type theorem; asymptotical stability; numerical methods
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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 theta-methods with constant stepsize are obtained. As a result Z. Jackiewicz's conjecture is partially proved. Finally, some experiments are given.
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