A Two Point Difference Scheme of an Arbitrary Order of Accuracy for BVPS for Systems of First Order Nonlinear Odes
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| 024 | 7 | 0 | |a 10.2478/cmam-2004-0026 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.2478/cmam-2004-0026 | ||
| 245 | 0 | 2 | |a A Two Point Difference Scheme of an Arbitrary Order of Accuracy for BVPS for Systems of First Order Nonlinear Odes |h [Elektronische Daten] |
| 520 | 3 | |a 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. | |
| 540 | |a This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. | ||
| 700 | 1 | |a Makarov |D V.L. |u Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601, Ukraine. | |
| 700 | 1 | |a Gavrilyuk |D I.P. |u Berufsakademie Thüringen, Staatliche Studienakademie, Am Wartenberg 2, D-99817 Eisenach, Germany. | |
| 700 | 1 | |a Kutniv |D M.V. |u Institute of Applied Mathematics, Lviv Polytechnical National University, 12 Bandery Str., 79013, Lviv-13, Ukraine. | |
| 700 | 1 | |a Hermann |D M. |u Friedrich Schiller University at Jena, Institute of Applied Mathematics, Ernst-Abbe-Platz 1{4, D-07740 JENA, Germany. | |
| 773 | 0 | |t Computational Methods in Applied Mathematics |d De Gruyter |g 4/4(2004), 464-493 |x 1609-4840 |q 4:4<464 |1 2004 |2 4 |o cmam | |
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| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Makarov |D V.L. |u Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601, Ukraine | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Gavrilyuk |D I.P. |u Berufsakademie Thüringen, Staatliche Studienakademie, Am Wartenberg 2, D-99817 Eisenach, Germany | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Kutniv |D M.V. |u Institute of Applied Mathematics, Lviv Polytechnical National University, 12 Bandery Str., 79013, Lviv-13, Ukraine | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Hermann |D M. |u Friedrich Schiller University at Jena, Institute of Applied Mathematics, Ernst-Abbe-Platz 1{4, D-07740 JENA, Germany | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Computational Methods in Applied Mathematics |d De Gruyter |g 4/4(2004), 464-493 |x 1609-4840 |q 4:4<464 |1 2004 |2 4 |o cmam | ||
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