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On the Exponential Convergence of Spline Approximation Methods for Wiener‐Hopf Equations

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  • Johannes Elschner

Abstract

We consider the approximate solution of Wiener‐Hopf integral equations by Galerkin, collocation and Nyström methods based on piecewise polynomials where accuracy is achieved by increasing simultaneously the number of mesh points and the degree of the polynomials. We look for the stability of those methods in the Lq norm, 1≤q≤∞. Provided the exact solution is analytic on the half‐axis and decays exponentially at infinity, we prove an exponential rate of convergence with respect to the number of degrees of freedom.

Suggested Citation

  • Johannes Elschner, 1993. "On the Exponential Convergence of Spline Approximation Methods for Wiener‐Hopf Equations," Mathematische Nachrichten, Wiley Blackwell, vol. 160(1), pages 253-264.
    • Handle: RePEc:bla:mathna:v:160:y:1993:i:1:p:253-264
    DOI: 10.1002/mana.3211600111
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