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

Advances in Difference Equations volume 2006, Article number: 012167 (2006) Cite this article

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 and Affiliations

  1. Berufsakademie Thüringen, Staatliche Studienakademie, Am Wartenberg 2, Eisenach, 99817, Germany

    IP Gavrilyuk

  2. Institute of Applied Mathematics, Friedrich Schiller University, Ernst-Abbe-Platz 1-4, Jena, 07740, Germany

    M Hermann

  3. Lviv Polytechnic National University, 12 St. Bandery Street, Lviv, 79013, Ukraine

    MV Kutniv

  4. Department of Numerical Analysis, Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka Street, Kyiv-4, 01601, Ukraine

    VL Makarov

Authors
  1. IP Gavrilyuk
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  2. M Hermann
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  4. VL Makarov
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Correspondence to IP Gavrilyuk.

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Gavrilyuk, I., Hermann, M., Kutniv, M. et al. Difference schemes for nonlinear BVPs using Runge-Kutta IVP-solvers. Adv Differ Equ 2006, 012167 (2006). https://doi.org/10.1155/ADE/2006/12167

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