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Applicable Analysis
An International Journal
Volume 63, 1996 - Issue 1-2
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Original Articles

Error bounds of discretization methods for boundary integral equations with noisy data

Gottfried Bruckner Institute of Mathematics, Otakaari 1, SF-02150 Espoo, Finland
,
Siegfried Prössdorf Institute of Mathematics, Otakaari 1, SF-02150 Espoo, Finland
&
Gennadi Vainikko Institute of Mathematics, Otakaari 1, SF-02150 Espoo, Finland
Pages 25-37 | Received 01 Mar 1996, Published online: 20 Jan 2011

References

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  • Hsiao , G.C. and Pröβdorf , S. 1988 . On the stability of the spline collocation method for a class of integral equations of the first kind . Applicable Analysis , 30 : 249 – 261 .
  • Hsiao , G.C. and Wendland , W.L. 1977 . A finite element method for some integral equations of the first kind . J. Math. Anal. and Appl. , 58 : 449 – 481 .
  • Hsiao , G.C. and Wendland , W.L. 1981 . The Aubin-Nitsche lemma for integral equations . J. Int. Equat. , 3 : 315
  • McLean , W. , Pröβdorf , S. and Wendland , W.L. 1989 . Pointwise error estimates for the trigonometric collocation method applied to singular integral equations and periodic pseudodifferential equations . J. Integral Equations Appl. , 2 : 125 – 146 .
  • McLean , W. , Pröβdorf , S. and Wendland , W.L. 1993 . A fully-discrete trigonometric collocation method . J. Integral Equations Appl. , 5 : 103 – 129 .
  • Natterer , F. 1977 . Regularisierung schlecht gestellter Probleme durch Projektionsverfahren . Numer. Math. , 28 : 329 – 341 .
  • Pröβdorf , S. and Silbermann , B. Numerical Analysis for Integral and Related Operator Equations , 1 – 542 . Berlin : Akademie-Verlag . Birkhäuser-Verlag,Basel,Boston,Stuttgart 1991
  • Saranen , J. 1993 . A modified discrete spectral collocation method for first kind integral equations with logarithmic kernel . J. Integral Equations Appl. , 5 : 547 – 567 .
  • Saranen , J. and Schroderus , L. 1994 . The modified quadrature method for classical pseudodifferential equations of negative order on smooth closed curves . J. Comput. Appl. Math. , 50 : 485 – 495 .
  • Saranen , J. and Schroderus , L. 1993 . Quadrature methods for strongly elliptic equations of negative order on smooth closed curves . SIAM J. Numer. Anal. , 30 : 1769 – 1795 .
  • Vainikko , G.M. and Hämarik , U.A. 1985 . Projection methods and self-regularization of ill-posed problems . Iz. VUZ. Mat. , 29 : 1 – 17 .

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