A collocation formulation of multistep methods for variable step-size extensions (Q1612439)
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scientific article; zbMATH DE number 1787719
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A collocation formulation of multistep methods for variable step-size extensions |
scientific article; zbMATH DE number 1787719 |
Statements
A collocation formulation of multistep methods for variable step-size extensions (English)
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22 August 2002
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Collocation methods are defined and formalized for the Cauchy problem of ordinary differential equations. The authors prove that a \(k\)-step variable formula is of order \(k+1\) if and only if it has a piecewise polynomial collocation formulation. The relation between the authors' methods, the Nordsieck formulation and Skeel's variable step-size extensions and Adams-Moulton methods is also shown.
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comparison of methods
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collocation methods
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Cauchy problem
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variable step-size
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Adams-Moulton methods
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