Using resolvent conditions to obtain new stability results for \(\theta\)-methods for delay differential equations (Q2713137)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Using resolvent conditions to obtain new stability results for \(\theta\)-methods for delay differential equations |
scientific article |
Statements
6 May 2001
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\(\theta\)-method
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Delay-differential equations
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stability region
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error growth
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linear test problems
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Using resolvent conditions to obtain new stability results for \(\theta\)-methods for delay differential equations (English)
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The author establishes upper bounds for the growth of errors in two numerical processes, viz., one-stage \(\theta\)-method and two-stage \(\theta\)-method, for solving delay-differential equations. In solving linear test problems of the form NEWLINE\[NEWLINEz'(t)=\lambda z(t)+ \mu z(t-r)NEWLINE\]NEWLINE with the help of \(\theta\)-methods, it is shown that the errors grow at most linearly with the number of time steps and with the dimension involved. An attempt is made to find out whether this kind of error growth is valid uniformly within the stability regions of these methods. Some unsolved problems are stated.
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