On the Convergence of the Finite Difference Method for Nonlinear Ordinary Boundary Value Problems

  • Wolf-Jürgen Beyn
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Serie Internationale D’Analyse Numerique book series (ISNM, volume 48)


There are well known conditions which finite difference equations approximating a linear ordinary boundary value problem have to satisfy in order to guarantee consistency and stability of the method and hence convergence of the finite difference solutions. Furthermore, under analogous assumptions a local convergence theorem holds in the nonlinear case. In this paper we give two global versions of this local result, one which yields a global stability inequality for the finite difference equations and another one which shows that the number of solutions is the same for the difference equations as for the boundary value problem. Our results are illustrated by two examples.


Local Result Linear Scheme Finite Difference Equation Root Condition Finite Difference Solution 
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Copyright information

© Springer Basel AG 1979

Authors and Affiliations

  • Wolf-Jürgen Beyn
    • 1
  1. 1.Institut für Numerische und instrumentelle MathematikUniversität MünsterMünsterGermany

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