Numerical analysis for one-dimensional Cauchy singular integral equations

Journal of Computational and Applied Mathematics

Volumn 125, Issue 1-2, 2000, Pages 395-421

  Junghanns, Peter ^a   Silbermann, Bernd ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL ANALYSIS; PROBLEM SOLVING;

BESOV SPACES; CAUCHY SINGULAR INTEGRAL EQUATIONS;

INTEGRAL EQUATIONS;

EID: 0034517489     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00482-9     Document Type: Article

References (24)

1. B.A. Amosov, On the approximate solution of elliptic pseudodifferential equations on smooth curves, Z. Anal. Anwendungen 9 (1990) 545-563 (in Russian).
2. D. Berthold, W. Hoppe, B. Silbermann, A fast algorithm for solving the generalized airfoil equation, J. Comput. Appl. Math. 43 (1992) 185-219.
3. D. Berthold, B. Silbermann, Corrected collocation methods for periodic pseudodifferential equations, Numer. Math. 70 (1995) 397-425.
4. D. Berthold, B. Silbermann, The fast solution of periodic pseudodifferential equations, Appl. Anal. 63 (1996) 3-23.
5. M.R. Capobianco, G. Criscuolo, P. Junghanns, A fast algorithm for Prandtl's integro-differential equation, J. Comput. Appl. Math. 77 (1997) 103-128.
6. M.R. Capobianco, G. Criscuolo, P. Junghanns, U. Luther, Uniform convergence of the collocation method for Prandtl's integro-differential equation, Proceedings of the David Elliott Conference, Hobart, 1997.
7. M.R. Capobianco, P. Junghanns, U. Luther, G. Mastroianni, Weighted uniform convergence of the quadrature method for Cauchy singular integral equations, in: A. Bottcher, I. Gohberg (Eds.), Singular Integral Operators and Related Topics, Birkhäuser, Basel, 1996, pp. 153-181.
8. I. Gohberg, N. Krupnik, One-Dimensional Linear Singular Integral Equations, Birkhäuser, Basel, 1992.
9. R. Hagen, S. Roch, B. Silbermann, Spectral Theory of Approximation Methods for Convolution Equations, Birkhäuser, Basel, 1994.
10. G. Heinig, K. Rost, Algebraic Methods for Toeplitz-like Matrices and Operators, Birkhäuser, Basel, 1984.
11. P. Junghanns, Product integration for the generalized airfoil equation, in: E. Schock (Ed.), Beiträge zur Angewandten Analysis und Informatik, Shaker Verlag, 1994, pp. 171-188.
12. P. Junghanns, U. Luther, Cauchy singular integral equations in spaces of continuous functions and methods for their numerical solution, J. Comput. Appl. Math. 77 (1997) 201-237.
13. P. Junghanns, U. Luther, Uniform convergence of a fast algorithm for Cauchy singular integral equations, Linear Algebra Appl. 275-276 (1998) 327-347.
14. P. Junghanns, U. Luther, Uniform convergence of the quadrature method for Cauchy singular integral equations with weakly singular perturbation kernels, Proceedings of the Third International Conference on Funct. Anal. Appr. Theory, Maratea, 1996, Vol. II, pp. 551-566.
15. P. Junghanns, G. Mastroianni, On the stability of collocation methods for Cauchy singular integral equations on an interval, to appear in: Operator Theory, Advances and Applications (Proceedings of the 11th TMP, Chemnitz, 1999), Birkhäuser, Basel.
16. P. Junghanns, K. Müller, A collocation method for nonlinear Cauchy singular integral equations, J. Comput. Appl. Math. 115 (2000) 283-300.
17. P. Junghanns, S. Roch, B. Silbermann, Stability of collocation methods for systems of Cauchy singular integral equations on an interval, in preparation.
18. P. Junghanns, U. Weber, Banach algebra techniques for Cauchy singular integral equations on an interval, in: J.I. Frankel, C.A. Brebbia, M.A.H. Aliabadi (Eds.), Boundary Element Technology XII, Computational Mechanics Publications, Southampton, Boston, 1997, pp. 419-428.
19. P. Junghanns, U. Weber, Local theory of projection methods for Cauchy singular integral equations on an interval, in: M. Golberg (Ed.), Boundary Integral Methods: Numerical and Mathematical Aspects, Computational Mechanics Publications, Series: Computational Engineering, Vol. 1, Boston, Southampton, 1998, pp. 217-256.
20. G. Monegato, S. Prössdorf, Uniform convergence estimates for a collocation and a discrete collocation method for the generalized airfoil equation, in: A.G. Agarval (Ed.), Contributions to Numerical Mathematics, World Scientific, Singapore, 1993, pp. 285-299.
21. S. Prössdorf, B. Silbermann, Numerical Analysis for Integral and Related Operator Equations, Birkhäuser, Basel, 1991.
22. S. Roch, Lokale Theorie des Reduktionsverfahrens für singuläre Integraloperatoren mit Carlemanschen Verschiebungen, Ph.D. Thesis, TU Karl-Marx-Stadt (now Chemnitz), 1987.
23. S. Roch, B. Silbermann, Asymptotic Moore-Penrose invertibility of singular integral operators, Integral Equations Operator Theory 26 (1996) 81-101.
24. J. Saranen, G. Vainikko, Fast solvers of integral and pseudodifferential equations on closed curves, Math. Comp. 67 (1998) 1473-1491.