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

Autor: Hermann M, Makarov VL, Kutniv MV, Gavrilyuk IP
Jazyk: angličtina
Rok vydání: 2006
Předmět:
Zdroj: Advances in Difference Equations, Vol 2006, Iss 1, p 012167 (2006)
Druh dokumentu: article
ISSN: 1687-1839
1687-1847
Popis: 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.
Databáze: Directory of Open Access Journals
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