ITERATED DEFECT CORRECTION FOR THE SOLUTION OF SINGULAR INITIAL VALUE PROBLEMS.
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| Title: | ITERATED DEFECT CORRECTION FOR THE SOLUTION OF SINGULAR INITIAL VALUE PROBLEMS. |
|---|---|
| Authors: | Koch, Othmar1 othmar@fsmat.htu.tuwien.ac.at, Weinmüller, Ewa B.1 e.weinmueller@tuwien.ac.at |
| Source: | SIAM Journal on Numerical Analysis. 2001, Vol. 38 Issue 6, p1784-1799. 16p. |
| Subjects: | Defect correction methods (Numerical analysis), Iterative methods (Mathematics), Stochastic convergence, Euler's numbers, Differential equations, Initial value problems, Approximation theory |
| Abstract: | We investigate the convergence properties of the iterated defect correction (IDeC) method based on the implicit Euler rule for the solution of singular initial value problems with a singularity of the first kind. We show that the method retains its classical order of convergence, which means that the sequence of approximations obtained during the iteration shows gradually growing order of convergence limited by the smoothness of the data and technical details of the procedure. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Numerical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 12682209 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: ITERATED DEFECT CORRECTION FOR THE SOLUTION OF SINGULAR INITIAL VALUE PROBLEMS. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Koch%2C+Othmar%22">Koch, Othmar</searchLink><relatesTo>1</relatesTo><i> othmar@fsmat.htu.tuwien.ac.at</i><br /><searchLink fieldCode="AR" term="%22Weinmüller%2C+Ewa+B%2E%22">Weinmüller, Ewa B.</searchLink><relatesTo>1</relatesTo><i> e.weinmueller@tuwien.ac.at</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Numerical+Analysis%22">SIAM Journal on Numerical Analysis</searchLink>. 2001, Vol. 38 Issue 6, p1784-1799. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Defect+correction+methods+%28Numerical+analysis%29%22">Defect correction methods (Numerical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+convergence%22">Stochastic convergence</searchLink><br /><searchLink fieldCode="DE" term="%22Euler's+numbers%22">Euler's numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Initial+value+problems%22">Initial value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We investigate the convergence properties of the iterated defect correction (IDeC) method based on the implicit Euler rule for the solution of singular initial value problems with a singularity of the first kind. We show that the method retains its classical order of convergence, which means that the sequence of approximations obtained during the iteration shows gradually growing order of convergence limited by the smoothness of the data and technical details of the procedure. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Numerical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/S0036142900368095 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 1784 Subjects: – SubjectFull: Defect correction methods (Numerical analysis) Type: general – SubjectFull: Iterative methods (Mathematics) Type: general – SubjectFull: Stochastic convergence Type: general – SubjectFull: Euler's numbers Type: general – SubjectFull: Differential equations Type: general – SubjectFull: Initial value problems Type: general – SubjectFull: Approximation theory Type: general Titles: – TitleFull: ITERATED DEFECT CORRECTION FOR THE SOLUTION OF SINGULAR INITIAL VALUE PROBLEMS. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Koch, Othmar – PersonEntity: Name: NameFull: Weinmüller, Ewa B. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: 2001 Type: published Y: 2001 Identifiers: – Type: issn-print Value: 00361429 Numbering: – Type: volume Value: 38 – Type: issue Value: 6 Titles: – TitleFull: SIAM Journal on Numerical Analysis Type: main |
| ResultId | 1 |
