Difference Schemes for Nonlinear BVPS on the Semiaxis
Abstract: The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Difference Schemes for Nonlinear BVPS on the Semiaxis ; volume:7 ; number:1 ; year:2007 ; pages:25-47
Computational methods in applied mathematics ; 7, Heft 1 (2007), 25-47
- Creator
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Gavrilyuk, I.P.
Hermann, M.
Kutniv, M.V.
Makarov, V.L.
- DOI
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10.2478/cmam-2007-0002
- URN
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urn:nbn:de:101:1-2410261628215.172139416794
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:29 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Gavrilyuk, I.P.
- Hermann, M.
- Kutniv, M.V.
- Makarov, V.L.
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