Some numerical methods for second-kind Fredholm integral equations on the real semiaxis

IMA Journal of Numerical Analysis

Volumn 29, Issue 4, 2009, Pages 1046-1066

  Mastroianni, Giuseppe ^a   Milovanović, Gradimir V ^b  

^a UNIVERSITY OF BASILICATA   (Italy)

^b Megatrend University Belgrade   (Serbia)

Author keywords

Error estimate; Fredholm integral equation; Gaussian quadrature formula; Generalized Laguerre weight function; Kernel; Lagrange interpolation; Nystr m interpolation; Orthogonal polynomials; Truncation

Indexed keywords

INTERPOLATION; NUMERICAL METHODS; ORTHOGONAL FUNCTIONS; POLYNOMIALS;

ERROR ESTIMATES; FREDHOLM INTEGRAL EQUATIONS; GAUSSIAN QUADRATURE FORMULA; GENERALIZED LAGUERRE WEIGHT FUNCTION; KERNEL; LAGRANGE INTERPOLATIONS; ORTHOGONAL POLYNOMIAL; TRUNCATION;

INTEGRAL EQUATIONS;

EID: 71049154481     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drn056     Document Type: Article

References (16)

1. ATKINSON, K. E. (1997) The Numerical Solution of Integral Equations of the Second Kind, Cambridge Monographs on Applied and Computational Mathematics. Cambridge: Cambridge University Press.
2. CVETKOVÍC, A. S. & MILOVANOVÍC, G. V. (2004) The Mathematica Package "OrthogonalPolynomials". Facta Univ. Ser. Math. Inform., 19, 17-36.
3. DE BONIS, M. C. & MASTROIANNI, G. (2006) Projection methods and condition numbers in uniform norm for Fredholm and Cauchy singular integral equations. SIAM J. Numer. Anal., 44, 1351-1374.
4. DE BONIS, M. C., MASTROIANNI, G. & VIGGIANO, M. (2002) K-functionals, moduli of smoothness and weighted best approximation on the semiaxis. Functions, Series, Operators (L. Leindler, F. Schipp & J. Szabados eds). Budapest: Janos Bolyai Mathematical Society, pp. 181-211.
5. DELLA VECCHIA, B. & MASTROIANNI, G. (2003) Gaussian rules on unbounded intervals. J. Complex., 19, 247-258.
6. JUNGHANNS, P. & SILBERMANN, B. (1981) Zur Theorie der Näherungsverfahren für singuläre Integralgleichungen auf Intervallen. Math. Nachr., 103, 199-244.
7. JUNGHANNS, P. & SILBERMANN, B. (1986) The numerical treatment of singular integral equations by means of polynomial approximations. Preprint P-MAT-35/86. Berlin: AdW der DDR, Karl Weierstrass Institut für Mathematik.
8. LEVIN, A. L. & LUBINSKY, D. S. (1992) Christoffel functions, orthogonal polynomials and Nevai's conjecture for Freud weights. Constr. Approx., 8, 463-535.
9. MASTROIANNI, G. & MONEGATO, G. (2003) Truncated quadrature rules over (0,1) and Nyström type methods. SIAM J. Numer. Anal., 41, 1870-1892.
10. MASTROIANNI, G. & OCCORSIO, D. (2004) Markov-Sonin Gaussian rule for singular functions. J. Comput. Appl. Math., 169, 197-212.
11. MASTROIANNI, G. & OCCORSIO, D. (2007) Mean convergence of Fourier sums on unbounded intervals. Stud. Univ. Babeş-Bolyai Math., 52, 89-103.
12. MASTROIANNI, G. & SZABADOS, J. (2007) Polynomial approximation on the real semiaxis with generalized Laguerre weights. Stud. Univ. Babeş-Bolyai Math., 52, 105-128.
13. MASTROIANNI, G. & V́ERTESI, P. (2006) Fourier sums and Lagrange interpolation on (0,+1) and (-1,+1). Frontiers in Interpolation and Approximation (N. K. Govil, H. N. Mhaskar, R. N. Mohapatra, Z. Nashed & J. Szabados eds). Boca Raton, FL: Taylor & Francis Books, pp. 307-344. (Dedicated to the memory of A. Sharma.)
14. MIKHLIN, S. G. & PRöSSDORF, S. (1986) Singular Integral Operators. Berlin: Akademie.
15. PRöSSDORF, S. & SILBERMANN, B. (1991) Numerical Analysis for Integral and Related Operator Equations. Berlin: Akademie.
16. SLOAN, I. M. (1988) A quadrature-based approach to improving the collocation method. Numer. Math., 54, 41-56.