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Numerische Mathematik

, Volume 23, Issue 2, pp 167–174 | Cite as

On the convergence of the von Neumann difference approximation to hyperbolic initial boundary value problems

  • E. Gekeler
Article

Abstract

The general implicit finite-difference approximation of second order devised by von Neumann is applied to the initial boundary value problem for a somewhat generalized wave equation. By means of eigenvalue expansion it is shown that the method is uniform convergent of order
$$\log \left( {\Delta x^{ - 1} } \right)O\left( {\Delta t^2 + \Delta x^2 } \right)$$
Δt, Δx mesh widths). Moreover, the convergence on the linet=T reveals to be proportional toT.

Keywords

Wave Equation Mathematical Method Difference Approximation Initial Boundary Mesh Width 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • E. Gekeler
    • 1
  1. 1.Mathem. Institut der UniversitätStuttgart 80Bundesrepublik Deutschland

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