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Delay-dependent stability of high order Runge–Kutta methods.
- Source :
- Numerische Mathematik; Jan2009, Vol. 111 Issue 3, p377-387, 11p
- Publication Year :
- 2009
-
Abstract
- Abstract  This paper is concerned with the study of the delay-dependent stability of Runge–Kutta methods for delay differential equations. First, a new sufficient and necessary condition is given for the asymptotic stability of analytical solution. Then, based on this condition, we establish a relationship between τ(0)-stability and the boundary locus of the stability region of numerical methods for ordinary differential equations. Consequently, a class of high order Runge–Kutta methods are proved to be τ(0)-stable. In particular, the τ(0)-stability of the Radau IIA methods is proved. [ABSTRACT FROM AUTHOR]
- Subjects :
- CALCULUS
MATHEMATICAL analysis
MATHEMATICAL functions
INFINITESIMAL geometry
Subjects
Details
- Language :
- English
- ISSN :
- 0029599X
- Volume :
- 111
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Numerische Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 35976606
- Full Text :
- https://doi.org/10.1007/s00211-008-0197-z