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

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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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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Keywords

  • Differential Equation
  • Exact Solution
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis