Abstract
We analyze the asymptotic stability of collocation solutions in spaces of globally continuous piecewise polynomials on uniform meshes for linear delay differential equations with vanishing proportional delay qt (0<q<1) (pantograph DDEs). It is shown that if the collocation points are such that the analogous collocation solution for ODEs is A-stable, then this asymptotic behaviour is inherited by the collocation solution for the pantograph DDE.
Original language | English |
---|---|
Pages (from-to) | 693-711 |
Number of pages | 19 |
Journal | BIT Numerical Mathematics |
Volume | 50 |
Issue number | 4 |
DOIs | |
Publication status | Published - Dec 2010 |
Scopus Subject Areas
- Software
- Computer Networks and Communications
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- Asymptotic stability on uniform meshes
- Collocation methods
- Delay differential equations
- Implicit Runge-Kutta methods
- Pantograph equation
- Proportional vanishing delay