Richard M. Karp, Raymond E. Miller
Journal of Computer and System Sciences
In this paper we study discretizations of the general pantograph equation y’(t) = ay(t) + by(θ(t)) + cy’(∅(t)) , t≥0, y(0)=y0where a , b , c , and y0are complex numbers and where θ and ∅ a re strictly increasing functions on the nonnegative reals with θ(0) = ∅(0) = 0 and θ(t) < t, ∅(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 ynn=0∞’s DOunded or that it tends to zero algebraically, as a negative power of n. © 1993 American Mathematical Society.
Richard M. Karp, Raymond E. Miller
Journal of Computer and System Sciences
Simeon Furrer, Dirk Dahlhaus
ISIT 2005
F. Odeh, I. Tadjbakhsh
Archive for Rational Mechanics and Analysis
Ziv Bar-Yossef, T.S. Jayram, et al.
Journal of Computer and System Sciences