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Order stars and stability for delay differential equations.
- Source :
- Numerische Mathematik; Sep1999, Vol. 83 Issue 3, p371-383, 13p
- Publication Year :
- 1999
-
Abstract
- We consider Runge–Kutta methods applied to delay differential equations $y'(t)=ay(t)+by(t-1)$ with real a and b. If the numerical solution tends to zero whenever the exact solution does, the method is called $\tau (0)$ -stable. Using the theory of order stars we characterize high-order symmetric methods with this property. In particular, we prove that all Gauss methods are $\tau (0)$ -stable. Furthermore, we present sufficient conditions and we give evidence that also the Radau methods are $\tau (0)$ -stable. We conclude this article with some comments on the case where a and b are complex numbers. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0029599X
- Volume :
- 83
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Numerische Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 49989330
- Full Text :
- https://doi.org/10.1007/s002110050454