Stability analysis of numerical methods for delay differential equations. (English) Zbl 0724.65084
This paper deals with the stability analysis of step-by-step methods for the numerical solution of delay differential equations. We focus on the behaviour of such methods when they are applied to the linear test problem \(U'(t)=\lambda U(t)+\mu U(t-\tau)\) with \(\tau >0\) and \(\lambda\), \(\mu\) complex. A general theorem is presented which can be used to obtain complete characterizations of the stability regions of these methods.
Reviewer: M.N.Spijker (Leiden)
MSC:
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 34K05 | General theory of functional-differential equations |
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