Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

# Advanced Search

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1063.65070
Yang, Zhanwen; Liu, Mingzhu; Song, Minghui
Stability of Runge-Kutta methods in the numerical solution of equation $u'(t)=au(t)+a_{0} u([t])+a_{1} u([t-1])$.
(English)
[J] Appl. Math. Comput. 162, No. 1, 37-50 (2005). ISSN 0096-3003

The authors discuss the numerical solution of the initial value problem $u'(t) = a u(t) + a_0 u([t]) + a_1 u([t-1])$, $u(0) = u_0$, $u(-1) = u_{-1}$, where $[\cdot]$ denotes the floor function (round down to nearest integer). This is a special case of a delay differential equation with piecewise continuous argument. The numerical methods under consideration are of Runge-Kutta type. The authors first explain how standard Runge-Kutta methods can be applied to this class of problems. Then, the asymptotic stability of various special types of Runge-Kutta methods (e.g., Gauss, Lobatto, and Radau) is investigated.
[Kai Diethelm (Braunschweig)]
MSC 2000:
*65L20 Stability of numerical methods for ODE
65L06 Multistep, Runge-Kutta, and extrapolation methods
65L10 Boundary value problems for ODE (numerical methods)
34K28 Numerical approximation of solutions of FDE

Keywords: delay differential equation; piecewise continuous argument; Runge-Kutta method; asymptotic stability

Login Username: Password:

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster