Global polynomial approximation for Symm's equation on polygons

Numerische Mathematik

Volumn 86, Issue 4, 2000, Pages 655-683

  Monegato, G ^a   Scuderi, L ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034364118     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005414     Document Type: Article

References (29)

1. Abaci C. (1994): The Scientific Desk Library Documentation System. Raleigh. North Carolina
2. Berthold D., Hoppe W., Silbermann B. (1992): A fast algorithm for solving the generalized airfoil equation. J. Comput. Appl. Math. 43, 185-219
3. Costabel M., Stephan E.P. (1987): On the convergence of collocation methods for boundary integral equations on polygons. Math. Comp. 49, 461-478
4. Elliott D., Prössdorf S. (1995): An algorithm for the approximate solution of integral equations of Mellin type. Numer. Math. 70, 427-452
5. Elschner J., private communication, 1998
6. Elschner J., Graham I.G. (1995): An optimal order collocation method for first kind boundary integral equations on polygons. Numer. Math. 70, 1-31
7. Elschner J., Graham I.G. (1995): Parametrization methods for first kind integral equations of nonsmooth boundaries. In: Dekker M., ed., Lecture Notes in Pure and Applied Mathematics Vol 167, New York, 81-99
8. Elschner J., Graham I.G. (1997): Quadrature methods for Symm's integral equation on polygons. IMA J. Numer. Anal. 17, 643-664
9. Elschner J., Prössdorf S., Sloan I.H. (1996): The qualocation method for Symm's integral equation on a polygon. Math. Nachr. 177, 81-108
10. Elschner J., Stephan E.P. (1996): A discrete collocation method for Symm's integral equation on curves with corners. J. Comput. Appl. Math. 75, 131-146
11. Graham I.G., Yan Y. (1991): Piecewise constant collocation for first kind boundary integral equations. J. Austral. Math. Soc. Ser. B 33, 39-64
12. Grisvard P. (1985): Elliptic Problems in Nonsmooth Domains. Pitman, Boston
13. Jeon Y., Sloan I.H., Stephan E.P., Elschner J. (1997): Discrete qualocation methods for logarithmic kernel integral equations on a piecewise smooth boundary. Adv. Comp. Math. 7, 547-571
14. Kress R. (1990): A Nyström method for boundary integral equations in domains with corners. Numer. Math. 58, 145-161
15. p error of Lagrange interpolation. J. Approx. Theory 82, 321-339
16. Maz'ya V.G. (1991): Boundary Integral Equations. In: Maz'ya V.G., Nikolskii S. M., eds., Analysis IV, Encyclopaedia of Mathematical Sciences Vol 27. Springer, Berlin
17. Monegato G., Scuderi L. (1998): High order methods for weakly singular integral equations with nonsmooth input functions. Math. Comp. 67, 1493-1515
18. Monegato G., Scuderi L. (1999): Numerical integration of functions with boundary singularities. J. Comput. Appl. Math. 112, 201-214
19. Monegato G., Sloan I.H. (1997): Numerical solution of the generalized airfoil equation for an airfoil with a flap. SIAM J. Numer. Anal. 34, 2288-2305
20. Prössdorf S., Rathsfeld A. (1989): Quadrature methods for strongly elliptic Cauchy singular integral equations on an interval. In: Dym H. et al., eds., Operator Theory: Advances and Applications, Vol 41. Birkhäuser, Basel
21. Prössdorf S., Silbermann B. (1991): Numerical Analysis for Integral and Related Operator Equations. Birkhäuser, Basel
22. Rathsfeld A. (1988): A quadrature method for a Cauchy singular integral equation with a fixed singularity. Seminar Analysis. Operator Equal., Numer. Anal. 1987/88, Karl-Weierstrasse-Inst. Math., Akad. Wiss. DDR, Berlin, 107-117
23. Rathsfeld A. (1996): Error estimates and extrapolation for the numerical solution of Mellin convolution equations. IMA J. Numer. Anal. 16, 217-255
24. Scuderi L. (1998): A collocation method for the generalized airfoil equation for an airfoil with a flap. SIAM J. Numer. Anal. 35, 1725-1739
25. Sloan I.H., Stephan E.P. (1992): Collocation with Chebyshev polynomials for Symm's integral equation on an interval. J. Austral. Math. Soc. Ser. B 34, 199-211
26. Szegö G. (1939): Orthogonal Polynomials. AMS Providence, Rhode Island
27. Yan Y. (1990): Cosine change of variable for Symm's integral equation on open arcs. IMA J. Numer. Anal. 10, 521-535
28. Yan Y, Sloan I.H. (1988): On integral equations of the first kind with logarithmic kernels. J. Integral Equations and Applications 1(4), 549-579
29. Yan Y., Sloan I.H. (1989): Mesh grading for integral equations of the first kind with logarithmic kernel. SIAM J. Numer. Anal. 26, 574-587