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 \(dy/dt=ay(t)+by(t-\tau)\) 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 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 35K05 | Heat equation |
Keywords:
asymptotic stability; stiff equation; Runge-Kutta methods; stability analysis; test equation; delay differential equations; backward Euler methods; Gauss collocation methodsReferences:
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