Iterated defect correction for the solution of singular initial value problems (Q2706389)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Iterated defect correction for the solution of singular initial value problems |
scientific article |
Statements
19 March 2001
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initial value problems
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singularity of the first kind
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convergence
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implicit Euler rule
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iterated defect correction
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convergence acceleration
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Iterated defect correction for the solution of singular initial value problems (English)
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This paper investigates the convergence properties of iterated defect correction based on the implicit Euler method and piecewise interpolation with polynomials of degree \(n\) for solving initial value problems with \(q\) singularity of the first kind of the form NEWLINE\[NEWLINEz'(t)= {1\over t} m(t) z(t)+ f(t,z(t)).NEWLINE\]NEWLINE The authors show that the convergence increases by one at each iteration, until order \(m\) is reached.
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