Open Access

Difference schemes for nonlinear BVPs using Runge-Kutta IVP-solvers

Advances in Difference Equations20062006:012167

https://doi.org/10.1155/ADE/2006/12167

Received: 11 November 2005

Accepted: 2 March 2006

Published: 26 June 2006

Abstract

Difference schemes for two-point boundary value problems for systems of first-order nonlinear ordinary differential equations are considered. It was shown in former papers of the authors that starting from the two-point exact difference scheme (EDS) one can derive a so-called truncated difference scheme (TDS) which a priori possesses an arbitrary given order of accuracy 0(|h| m ) with respect to the maximal step size |h|. This m-TDS represents a system of nonlinear algebraic equations for the approximate values of the exact solution on the grid. In the present paper, new efficient methods for the implementation of an m-TDS are discussed. Examples are given which illustrate the theorems proved in this paper.

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Authors’ Affiliations

(1)
Berufsakademie Thüringen, Staatliche Studienakademie
(2)
Institute of Applied Mathematics, Friedrich Schiller University
(3)
Lviv Polytechnic National University
(4)
Department of Numerical Analysis, Institute of Mathematics, National Academy of Sciences of Ukraine

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Copyright

© I. P. Gavrilyuk et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.