Stability of collocation methods for delay differential equations with vanishing delays
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- 作者：Hermann Brunner and Hui Liang
- 关键词：Delay differential equations ; Pantograph equation ; Proportional vanishing delay ; Collocation methods ; Implicit Runge ; Kutta methods ; Asymptotic stability on uniform meshes
- 刊名：BIT Numerical Mathematics
- 出版时间：December 2010
- 出版年：2010
- 期刊代码：30_0006-3835
- 类别：mat
- 卷：50
- 期：4
- 页码：693-711
- 数据来源：sp
摘要
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.