Journal of Integral Equations and Applications

Stability of Approximation Methods on Locally Non-Equidistant Meshes for Singular Integral Equations

V.D. Didenko and B. Silbermann

Full-text: Open access

Article information

Source
J. Integral Equations Applications Volume 11, Number 3 (1999), 317-349.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
http://projecteuclid.org/euclid.jiea/1181074281

Digital Object Identifier
doi:10.1216/jiea/1181074281

Mathematical Reviews number (MathSciNet)
MR1719091

Zentralblatt MATH identifier
0974.65121

Citation

Didenko, V.D.; Silbermann, B. Stability of Approximation Methods on Locally Non-Equidistant Meshes for Singular Integral Equations. J. Integral Equations Applications 11 (1999), no. 3, 317--349. doi:10.1216/jiea/1181074281. http://projecteuclid.org/euclid.jiea/1181074281.


Export citation

References

  • D.N. Arnold and W.L. Wendland, The convergence of spline-collocation for strongly elliptic equations on curves, Numer. Math. 47 (1985), 317-341.
  • S.M. Belotserkovski and I.K. Lifanov, Method of discrete vortices, CRC Press, Boca Raton, FL, 1993.
  • C. De Boor, A practical guide to splines, Springer-Verlag, New York, 1978.
  • K. Buehring, A quadrature method for singular integral equations on curves with corners, Math. Nachr. 167 (1994), 43-81.
  • M. Costabel and E. Stephan, Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximations, Banach Center Publ. 15, PWN, Warsaw (1985), 175-251.
  • V.D. Didenko, S. Roch and B. Silbermann, Approximation methods for singular integral equations with conjugation on curves with corners, SIAM J. Numer. Anal. 32 (1995), 1910-1939.
  • R. Duduchava, D. Elliott and W.L. Wendland, The spline collocation method for Mellin convolution operators, Bericht 96/04, Univ. Stuttgart, SFB 404.
  • D. Elliott and S. Prößdorf, An algorithm for the approximate solution of integral equations of Mellin type, J. Numer. Anal. 70 (1995), 427-452.
  • A. Erdelyi, W. Magnus, F. Oberhettinger and F. Tricomi, Tables of integral transforms, Vol. 1, McGraw-Hill Book Company, Inc., New York, 1954.
  • I.C. Gohberg and N.Ya. Krupnik, On the algebra generated by Toeplitz matrices, Funktsional Anal. i Prilozhen 3 (1969), 46-56, in Russian.
  • I.C. Gohberg and N.Ya. Krupnik, One dimensional singular integral equations, Vol. I-II, Oper. Theory Adv. Appl. 53-54, Birkhäuser-Verlag, Basel, 1992.
  • R. Hagen, S. Roch and B. Silbermann, Spectral theory of approximation methods for convolution equations, Oper. Theory. Adv. Appl. 74, Birkhäuser-Verlag, Basel, 1995.
  • R. Kress, Nyström method for boundary integral equations in domains with corners, Numer. Math. 58 (1990), 145-161.
  • S. Prößdorf and A. Rathsfeld, Mellin techniques in the numerical analysis for one-dimensional singular integral equations, Report R-MATH 06/88, Karl-Weierstrass-Inst., Berlin, 1988.
  • --------, Quadrature and collocation methods for singular integral equations on curves with corners, Z. Anal. Anwendungen 8 (1989), 197-220.
  • --------, Quadrature methods for strongly elliptic Cauchy singular integral equations on an interval, in Topics in analysis and operator theory, Vol. 2, The Gohberg Anniversary Collection (H. Dym, et al., eds.), Birkhäuser-Verlag, Basel, 1989.
  • S. Prößdorf and B. Silbermann, Numerical analysis for integral and related operator equations, Akademie-Verlag, Berlin, 1991, and Birkhäuser-Verlag, Basel, 1991.
  • S. Roch, Spline approximation method cutting off singularities, Z. Anal. Anwendungen 13 (1994), 329-345.
  • S. Roch and B. Silbermann, $C^*$-algebra techniques in numerical analysis, J. Operator Theory 35 (1996), 241-280.
  • B. Silbermann, Locale Theorie des Reduktionsverfahrens für Toeplitz-operatoren, Math. Nachr. 105 (1981), 137-146.
  • I.H. Sloan, A quadrature-based approach to improving the collocation method, Numer. Math. 654 (1988), 41-56.
  • I.H. Sloan and W.L. Wendland, A quadrature-based approach to improving the collocation method for splines of even degree, Z. Anal. Anwendungen 8 (1989), 361-376.
  • E. Venturino, Stability and convergence of a hyperbolic tangent method for singular integral equations, Math. Nachr. 164 (1993), 167-186.