A Two Point Difference Scheme of an Arbitrary Order of Accuracy for BVPS for Systems of First Order Nonlinear Odes
Abstract: We consider two-point boundary value problems for systems of first-order nonlinear ordinary differential equations. Under natural conditions we show that on an arbitrary grid there exists a unique two-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection onto the grid of the exact solution of the corresponding system of differential equations. A constructive algorithm is proposed in order to derive from the EDS a so-called truncated difference scheme of an arbitrary rank. The m-TDS represents a system of nonlinear algebraic equations with respect to the approximate values of the exact solution on the grid. Iterative methods for its numerical solution are discussed. Analytical and numerical examples are given which illustrate the theorems proved. Keywords: systems of nonlinear ordinary differential equations, difference scheme, exact difference scheme, truncated difference scheme of an arbitrary order of accuracy, fixed point iteration.
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Erschienen in
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A Two Point Difference Scheme of an Arbitrary Order of Accuracy for BVPS for Systems of First Order Nonlinear Odes ; volume:4 ; number:4 ; year:2004 ; pages:464-493
Computational methods in applied mathematics ; 4, Heft 4 (2004), 464-493
- Urheber
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Makarov, V.L.
Gavrilyuk, I.P.
Kutniv, M.V.
Hermann, M.
- DOI
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10.2478/cmam-2004-0026
- URN
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urn:nbn:de:101:1-2410261614542.007590680597
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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15.08.2025, 07:25 MESZ
Datenpartner
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Beteiligte
- Makarov, V.L.
- Gavrilyuk, I.P.
- Kutniv, M.V.
- Hermann, M.
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