Uniform convergence estimates for a collocation method for the cauchy singular integral equation

Journal of Integral Equations and Applications

Volumn 9, Issue 1, 1997, Pages 21-45

  Capobianco, M R ^a   Russo, M G ^b  

^a Ist per Applicazioni della M   (Italy)

^b UNIVERSITY OF BASILICATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039531945     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/jiea/1181075986     Document Type: Article

References (22)

1. K.E. Atkinson, A survey of numerical method for the solution of Fredholm integral equations of the second kind, SIAM, Philadelphia, Pennsylvania, 1976.
2. M.R. Capobianco, The stability and the convergence of a collocation method for a class of Cauchy singular integral equations, Math. Nachr. 162 (1993), 45-58.
3. M.R. Capobianco, P. Junghanns, U. Luther and G. Mastroianni, Weighted uniform convergence of the quadrature method for Cauchy singular integral equa tions, in Singular integral operators and related topics (A. Bottcher and I. Gohberg, ed.), Operator Theory Advances and Applications, Vol. 90, Birkhäuser Verlag, 1995, 153-181.
4. G. Criscuolo and G. Mastroianni, Convergence of Gauss type product formulas for the evaluation of two-dimensional Cauchy principal value integrals, Bit 27 (1987), 72-84.
5. G. Criscuolo, G. Mastroianni and P. Nevai, Associated generalized Jacobi functions and polynomials, J. Math. Anal. Appl. 158 (1991), 15-34.
6. G. Criscuolo, G. Mastroianni and P. Vertesi, Pointwise simultaneous conver gence of the extended Lagrange interpolation with additional knots, Math Comp. 59 (1992), 515-531.
7. D. Elliott, The classical collocation method for singular integral equations, SIAM J. Numer. Anal. 19 (1982), 816-832.
8. D. Elliott, Projection methods for singular integral equations, J. Integral Equa tions Appl. 2 (1989), 95-106.
9. F. Erdogan, G.D. Gupta and T.S. Cook, Numerical solution of singular integral equations, Mech. of Fracture 1 (1973), 368-425.
10. M.A. Golberg, The numerical solution of Cauchy singular integral equations with constant coefficients, J. Integral Equations 9 (1985), 127-152.
11. P. Junghanns, Product integration for the generalized airfoil equation, in Beiträge zur Angewandten Anlysis und Informatik (E. Schock, ed.), Shaker Verlag, Aachen, 1994, 171-188.
12. P. Junghanns and B. Silbermann, Zur Theorie der Näherungsverfahren fur singulare Integralgleichungen auf Intervalien, Math. Nachr. 103 (1981), 199-244.
13. P. Junghanns, Numerical analysis of the quadrature method for solving linear and nonlinear singular integral equations, Preprint, Technical University Chemnitz, (1989).
14. G. Mastroianni, Uniform convergence of the derivatives of Lagrange interpo lation, J. Comp. Appl. Math. 43 (1992), 37-51.
15. G. Mastroianni and S. Prößdorf, A quadrature method for Cauchy integral equations with weakly singular perturbation kernel, J. Integral Equations Appl. 4 (1992), 1-24.
16. S.G. Mikhlin and S. Prößdorf, Singular integral operators, Springer-Verlag, New York, 1986.
17. G. Monegato and S. Prößdorf, Uniform convergence estimates for a collo cation method for the generalized airfoil equation, in Contribution in numerical mathematics, Vol. II (R.P. Agarwal, ed.), (World Scientific Series in Applicable Analysis) 1993, 285-299.
18. N.I. Muskhelishvili, Singular integral equations, Noordhoff, Groningen, 1953.
19. P. Nevai, Mean convergence of Lagrange interpolation III, Trans. Amer. Math. Soc. 282 (1984), 669-698.
20. S. Prößdorf and B. Silbermann, Projektionsverfahren und die naherungsweise Losung singuldrer Gleichungen, Teubner Verlagsges., Leipzig, 1977.
21. S. Prößdorf, Numerical analysis for integral and related operator equations, Akademie-Verlag, Berlin, 1991 and Birkhauser Verlag, Boston, 1991.
22. E. Venturino, Recent developments in the numerical solution of singular integral equations, J. Math. Anal. Appl. 115 (1986), 239-277.