Journal of Integral Equations and Applications

A Fully-Discrete Trigonometric Collocation Method

W. McLean, S. Prössdorf, and W.L. Wendland

Full-text: Open access

Article information

J. Integral Equations Applications Volume 5, Number 1 (1993), 103-129.

First available in Project Euclid: 5 June 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


McLean, W.; Prössdorf, S.; Wendland, W.L. A Fully-Discrete Trigonometric Collocation Method. J. Integral Equations Applications 5 (1993), no. 1, 103--129. doi:10.1216/jiea/1181075730.

Export citation


  • B.A. Amosov, On the approximate solution of elliptic pseudo-differential equations on a smooth, closed curve, Z. Anal. Anwendungen 9 (1990), 545-563.
  • K.E. Atkinson, A discrete Galerkin method for the first kind integral equations with a logarithmic kernel, J. Integral Equations Appl. 1 (1988), 343-363.
  • K.E. Atkinson and I.H. Sloan, The numerical solution of first-kind logarithmic-kernel integral equations on smooth open arcs, Math. Comp. 56 (1991), 119-139.
  • J. Bergh and J. Löfström, Interpolation spaces: An introduction, Springer, Berlin, New York, 1976.
  • M. Costabel and W. McLean, Global symbols of boundary integral operators on a torus, Proc. Centre Math. Anal. Austral. Nat. Univ., to appear.
  • D. Gaier, Integralgleichungen erster Art und konforme Abbildungen, Math. Z. 147 (1976), 113-139.
  • W. Hackbusch, Multi-Grid methods and applications, Springer-Verlag, Berlin, 1985.
  • G. Hsiao, P. Kopp and W.L. Wendland, Some applications of a Galerkin-collocation method for boundary integral equations of the first kind, Math. Methods Appl. Sci. 6 (1984), 280-325.
  • G. Hsiao, E. Stephan and W.L. Wendland, On the Dirichlet problem in elasticity for a domain exterior to an arc, J. Comput. Appl. Math. 34 (1991), 1-19.
  • U. Lamp, T. Schleicher and W.L. Wendland, The fast Fourier transform and the numerical solution of one-dimensional boundary integral equations, Numer. Math. 47 (1985), 15-38.
  • W. McLean, Local and global descriptions of periodic pseudodifferential operators, Math. Nachr. 150 (1991), 151-161.
  • W. McLean, S.B. Prössdorf and W.L. Wendland, Pointwise error estimates for the trigonometric collocation method applied to singular integral equations and periodic pseudodifferential equations, J. Integral Equations Appl. 2 (1989), 125-146.
  • W. McLean and W.L. Wendland, Trigonometric approximation of solutions of periodic pseudodifferential equations, in The Gohberg anniversary collection, Oper. Theory: Adv. Appl. 41 (1989), 359-383.
  • J. Prestin, Trigonometric interpolation in Hölder spaces, J. Approx. Theory 53 (1988), 145-154.
  • S. Prössdorf, Zur Konvergenz der Fourierreihen Hölder-stetiger Funktionen, Math. Nachr. 69 (1975), 7-14.
  • S. Prössdorf and B. Silbermann, Projektionsverfahren und die näherungsweise Lösung singulärer Gleichungen, Teubner-Verlag, Leipzig, 1977.
  • --------, Numerical analysis for integral and related operator equations, Akademie-Verlag, Berlin, 1991, and Birkhäuser-Verlag, Basel, Boston, Stuttgart, 1991.
  • B. Silbermann, Approximation of solutions of periodic pseudodifferential equations and optimal error estimates, in Seminar analysis, operator equations and numerical analysis, 1988/89, Karl-Weierstraß-Institut für Mathematik, Berlin, 1989, 141-152.
  • H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam, New York, Oxford, 1978.
  • Y. Yan and I.H. Sloan, On integral equations of the first kind with logarithmic kernel, J. Integral Equations Appl. 1 (1988), 549-579.