caa a22 4500 378936735 CHVBK 20180305123642.0 cr unu---uuuuu 161128s2004 xx s 000 0 eng 10.2478/cmam-2004-0026 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2004-0026 A Two Point Difference Scheme of an Arbitrary Order of Accuracy for BVPS for Systems of First Order Nonlinear Odes [Elektronische Daten] 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. 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. Makarov V.L. Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601, Ukraine. Gavrilyuk I.P. Berufsakademie Thüringen, Staatliche Studienakademie, Am Wartenberg 2, D-99817 Eisenach, Germany. Kutniv M.V. Institute of Applied Mathematics, Lviv Polytechnical National University, 12 Bandery Str., 79013, Lviv-13, Ukraine. Hermann M. Friedrich Schiller University at Jena, Institute of Applied Mathematics, Ernst-Abbe-Platz 1{4, D-07740 JENA, Germany. Computational Methods in Applied Mathematics De Gruyter 4/4(2004), 464-493 1609-4840 4:4<464 2004 4 cmam https://doi.org/10.2478/cmam-2004-0026 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2004-0026 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Makarov V.L. Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601, Ukraine NATIONALLICENCE 700 1- Gavrilyuk I.P. Berufsakademie Thüringen, Staatliche Studienakademie, Am Wartenberg 2, D-99817 Eisenach, Germany NATIONALLICENCE 700 1- Kutniv M.V. Institute of Applied Mathematics, Lviv Polytechnical National University, 12 Bandery Str., 79013, Lviv-13, Ukraine NATIONALLICENCE 700 1- Hermann M. Friedrich Schiller University at Jena, Institute of Applied Mathematics, Ernst-Abbe-Platz 1{4, D-07740 JENA, Germany NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 4/4(2004), 464-493 1609-4840 4:4<464 2004 4 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter