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Original Articles

On fully discrete collocation methods for solving weakly singular integral equations

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Pages 69-78 | Received 30 Sep 2008, Published online: 14 Oct 2010

References

  • Brunner , H. 1985 . The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes . Math. Comp., , 45 : 417 – 437 .
  • Brunner , H. , Pedas , A. and Vainikko , G. 1999 . The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations . Math. Comp., , 68 (227) : 1079 – 1095 .
  • Kaneko , H. and Xu , Y. 1994 . Gauss‐Type quadratures for weakly singular integrals and their application to Fredholm integral equations of second kind . Math. Comp., , 62 : 739 – 753 .
  • Kangro , R. and Kangro , I. 2008 . On the stability of piecewise polynomial collocation methods for solving weakly singular integral equations of the second kind . Math. Model. Anal., , 13 (1) : 29 – 36 . (doi:10.3846/1392–6292.2008.13.29–36)
  • Parts , I. 2005 . “ Piecewise polynomial collocation methods for solving weakly singular integro‐differential equations ” . PhD thesis, Available from Internet: http://www.utlib.ee/ekollekt/diss/dok/2005/b1741779x/parts.pdf [cited 30 September 2008]
  • Pedas , A. and Vainikko , G. 1997 . Superconvergence of piecewise polynomial collocation for nonlinear weakly singular integral equations . J. Integral Equations Appl., , 9 : 379 – 406 .
  • Tamme , E. 2001 . Fully discrete collocation method for weakly singular integral equations . Proc. Estonian Acad. Sci. Phys. Math., , 50 (3) : 133 – 144 .
  • Vainikko , G. 1993 . Multidimensional Weakly Singular Integral Equations, Lecture Notes Math. , Berlin‐Heidelberg‐New York : Springer‐Verlag .
  • Vainikko , G. , Pedas , A. and Uba , P. 1984 . Methods for Solving Weakly Singular Integral Equations. , Tartu : Univ. of Tartu . (in Russian)
  • The work of Raul Kangro was partially supported by EstSF grant no. 7044. The work of Inga Kangro has been partially supported by Estonian Scientific Competence Council targeted financing grant No. 0140083s08

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