Error control for initial value problems with discontinuities and delays. (English) Zbl 0781.65061
The analysis of the error in numerical approximation is extended to a certain class of ordinary differential equation initial value problems with low-order derivative discontinuities and to the class of ordinary differential equations with constant delays. It is shown that standard error control techniques will be successful if discontinuities are handled correctly and delay terms are calculated with sufficiently accurate interpolants. The obtained theoretical results are illustrated numerically.
Reviewer: K.Najzar (Praha)
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
| 34K05 | General theory of functional-differential equations |
Keywords:
local error; global error; Runge-Kutta method; numerical example; initial value problems; discontinuities; delays; error controlReferences:
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