×

Iteration methods for Fredholm integral equations of the second kind. (English) Zbl 1127.65102

The authors investigate an efficient iteration algorithm for Fredholm integral equations of the second kind, and apply this algorithm to new projection methods: degenerate kernel methods using tensor products and orthogonal projections based on Galerkin methods and collocation methods.

MSC:

65R20 Numerical methods for integral equations
45B05 Fredholm integral equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Atkinson, K. E., The Numerical Solution of Integral Equations of the Second Kind (1997), Cambridge University Press: Cambridge University Press Cambridge, UK · Zbl 0155.47404
[2] Chatelin, F., Spectral Approximation of Linear Operators (1983), Academic Press: Academic Press New York · Zbl 0517.65036
[3] Chen, Z.; Xu, Y., The Petrov-Galerkin and iterated Petrov-Galerkin method for second kind integral equations, SIAM J. Numer. Anal., 35, 406-434 (1998) · Zbl 0911.65143
[4] Chen, Z.; Xu, Y.; Zhao, J., The discrete Petrov-Galerkin method for weakly singular integral equations, J. Integral Equations Appl., 11, 1-35 (1999) · Zbl 0974.65122
[5] Chen, Z.; Micchelli, C. A.; Xu, Y., A multilevel method for solving operator equations, J. Math. Anal. Appl., 262, 688-699 (2001) · Zbl 0990.65059
[6] Chen, Z.; Micchelli, C. A.; Xu, Y., Fast collocation methods for second kind integral equations, SIAM J. Numer. Anal., 40, 344-375 (2002) · Zbl 1016.65107
[7] Kress, R., Linear Integral Equations (1989), Springer-Verlag: Springer-Verlag Berlin
[8] N. Gnaneshwar, Spectral approximation for integral operators, Ph.D. Thesis, Indian Institute of Technology, Bombay, India, 2003; N. Gnaneshwar, Spectral approximation for integral operators, Ph.D. Thesis, Indian Institute of Technology, Bombay, India, 2003
[9] N. Gnaneshwar, A degenerate kernel method for eigenvalue problems of compact integral operators, Adv. Comput. Math. (in press); N. Gnaneshwar, A degenerate kernel method for eigenvalue problems of compact integral operators, Adv. Comput. Math. (in press) · Zbl 1127.65099
[10] Graham, I. G.; Joe, S.; Sloan, I. H., Iterated Galerkin versus iterated collocation for integral equations of second kind, IMA J. Numer. Anal., 5, 355-369 (1985) · Zbl 0586.65091
[11] Kaneko, H.; Xu, Y., Superconvergence of the iterated Galerkin methods for Hammerstein equations, SIAM J. Numer. Anal., 33, 1048-1064 (1996) · Zbl 0860.65138
[12] Kaneko, H.; Padilla, P.; Xu, Y., Superconvergence of the iterated degenerate kernel method, Appl. Anal., 80, 331-351 (2001) · Zbl 1020.65099
[13] Kulkarni, R. P.; Gnaneshwar, N., Spectral refinement using new projection method, ANZIAM J., 46, 203-224 (2004) · Zbl 1066.65062
[14] Porter, D.; Stirling, D. S.G., The reiterated Galerkin method, IMA J. Numer. Anal., 13, 125-139 (1993) · Zbl 0766.65048
[15] Sloan, I. H., Four variants of the Galerkin method for integral equations of the second kind, IMA J. Numer. Anal., 4, 9-17 (1984) · Zbl 0548.65093
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.