Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 30, 1988 - Issue 4
Submit an article Journal homepage
15
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

On the stability of the spline collocation method for a class of integral equations of the first kind

George C. Hsiao Department of Mathematical Sciences, University of Delaware, Newark, Delaware, 19716, USA
&
Siegfried Prössdorf Karl-Weierstrasse-lnstitut fur Mathematik, Akademie der Wissenschaften der DDR, GDR, 1086, Berlin
Pages 249-261 | Received 25 Sep 1988, Published online: 02 May 2007

References

  • Arnold , D.N. and Wendland , W.L. 1983 . On the asymptotic convergence of collocation methods . Math. Comp , 41 : 349 – 381 .
  • Arnold , D.N. and Wendland , W.L. 1985 . The convergence of spline colloca- tion for strongly elliptic equations on curves . Numer. Math , 47 : 317 – 341 .
  • Babuska , I. and Aziz , A.K. 1972 . Mathematical Foundation of the Finite Element Method with Applications to Partial Differential Equations , New York : Academic Press .
  • Elschner , J. and Schmidt , G. 1983 . On spline interpolation in periodic Sobolev spaces . Inst. Math., Akademie der Wissenschaften ,
  • Hsiao , G.C. and Wendland , W.L. 1977 . A finite element method for some integral equations of the first kind . J. Math. Anal. Appl , 58 : 449 – 481 .
  • Hsiao , G.C. 1983 . Improperly Posed Problems and Their Numerical Treatment , 117 – 131 . Basel : G. Hammerlin and K. H. Hoffmann,Birkhauser-Verlag .
  • Hsiao , G.C. 1986 . On the stability of integral equations of the first kind with logarithmic kernels . Arch. Rat. Mech. Anal , 94 : 179 – 192 .
  • Mikhlin , S.G. and Prossdorf , S. 1986 . Singular Integral Operators, Akademie-Verlag , New York : Berlin, and Springer-Verlag, Berlin, Heidelberg .
  • Natterer , F. 1977 . Regularisierung schlecht gestellter Probleme durch Projek- tionsverfahren . Numer. Math , 28 : 329 – 341 .
  • Prossdorf , S. and Silbermann , B. 1977 . Projektionsverfahren und die naherungsweise Losungsingularer Gleichungen , Leipzig : Teubner-Texte zur Mathematik, BSB B. G. Teubner Verlagsgesellschaft .
  • Rannacher , R. and Wendland , W.L. 1985 . On the order of pointwise con vergence of some boundary element methods. Part I: Operators of negative and zero order . Math. Modelling and Numer. Anal , 19 : 65 – 88 .
  • Schmidt , G. 1985 . On spline collocation methods for boundary integral equations in the plane . Math. Meth. Appl. Sci , 7 : 74 – 89 .
  • Wendland , W.L. and Christiansen , S. 1986 . On the condition number of the influence matrix belonging to some first kind integral equations with logarithmic kernel . Applic. Anal , 21 : 175 – 183 .
  • Wendland , W.L. 1985 . Asymptotic accuracy and convergence for point collocation methods . in Topics in Boundary Element Research , 2 : 230 – 257 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.