Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Stability of the discretized pantograph differential equation

Authors: Martin Buhmann and Arieh Iserles
Journal: Math. Comp. 60 (1993), 575-589
MSC: Primary 65L20; Secondary 34K20
MathSciNet review: 1176707
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study discretizations of the general pantograph equation

$\displaystyle y'(t) = ay(t) + by(\theta (t)) + cy'(\phi (t)),\quad t \geq 0,\quad y(0) = {y_0},$

, where a, b, c, and $ {y_0}$ are complex numbers and where $ \theta $ and $ \phi $ are strictly increasing functions on the nonnegative reals with $ \theta (0) = \phi (0) = 0$ and $ \theta (t) < t, \phi (t) < t$ for positive t. Our purpose is an analysis of the stability of the numerical solution with trapezoidal rule discretizations, and we will identify conditions on a, b, c and the stepsize which imply that the solution sequence $ \{ {y_n}\} _{n=0}^\infty $ is bounded or that it tends to zero algebraically, as a negative power of n.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L20, 34K20

Retrieve articles in all journals with MSC: 65L20, 34K20

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society