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


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.


Wave Equation Mathematical Method Difference Approximation Initial Boundary Mesh Width 
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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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