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Stability of numerical methods for delay differential equations. (English) Zbl 0664.65073
In the stability analysis of numerical methods for ordinary differential equations, the classical test equation $dy/dt=\lambda y$ has been supplemented in the last fifteen years by essentially more complex, nonlinear problems. In a similar vein, the author suggests nonlinear model problems that can supplement the equation $dy/dt=ay\left(t\right)+by\left(t-\tau \right)$ in the study of the stability of methods for delay differential equations. While the backward Euler methods is found to perform well when applied to the new tests, this is not so for the (A-stable) Gauss collocation methods.
Reviewer: J.M.Sanz-Serna

##### MSC:
 65L05 Initial value problems for ODE (numerical methods) 65L20 Stability and convergence of numerical methods for ODE 35K05 Heat equation