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On the Exponential Convergence of Spline Approximation Methods for Wiener‐Hopf Equations
Author(s) -
Elschner Johannes
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211600111
Subject(s) - mathematics , piecewise , mathematical analysis , rate of convergence , collocation method , exponential function , galerkin method , exponential polynomial , differential equation , nonlinear system , ordinary differential equation , channel (broadcasting) , physics , electrical engineering , quantum mechanics , engineering
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 L q 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.