A class of multiderivative hybrid one-step methods (Q1862825)
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scientific article; zbMATH DE number 1885791
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A class of multiderivative hybrid one-step methods |
scientific article; zbMATH DE number 1885791 |
Statements
A class of multiderivative hybrid one-step methods (English)
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30 November 2003
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This paper presents a class of hybrid one-step methods for initial value problems of ordinary differential equations. These methods involve the \(s\)th order derivative and \(s+ 1\) free parameters. The order of the algorithms satisfy \(s+ 1\leq p\leq 2s+ 2\). First, the cofficients of the methods are constructed. Then the stability properties are studied, necessary and sufficient conditions for \(A\)-stability and \(L\)-stability are derived. Finally, some methods of order 7, 8, and 10 and numerical results are given.
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implicit method
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hybrid one-step methods
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initial value problems
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algorithms
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\(A\)-stability
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\(L\)-stability
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numerical results
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