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Mathematical Modelling and Analysis Volume 5, 2000 - Issue 1
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Original Articles

Two‐grid iteration method for weakly singular integral equations

K. Hakk Institute of Applied Mathematics, University of Tartu, J. Liivi 2, Tartu, 50409, Estonia E-mail: [email protected]
&
A. Pedas Institute of Applied Mathematics, University of Tartu, J. Liivi 2, Tartu, 50409, Estonia E-mail: [email protected]
Pages 76-85 | Received 10 Oct 1999, Published online: 14 Oct 2010

References

  • Atkinson , K. E. 1992 . A survey of numerical methods for solving nonlinear integral equations . J. Integral Equations Appl. , 4 : 15 – 46 .
  • Atkinson , K. E. 1994 . Two‐grid iteration methods for linear integral equations of the second kind on piecewise smooth surfaces . R 3. SIAMJ.Sci. Comput. , 15 : 1083 – 1104 .
  • Atkinson , K. E. 1997 . The Numerical Solution of Integral Equations of the Second Kind , Cambridge University Press .
  • Hackbusch , W. 1985 . Multi‐Grid Methods and Applications , Berlin : Springer Verlag .
  • Hackbusch , W. 1989 . Integralgleichungen. Theorie und Numerik , Stuttgart : Teubner . English translation: Integral Equation. Theory and Numerical Methods. ISNM 120, Birkhäuser, Basel, 1995
  • Hakk , K. and Pedas , A. 1998 . “ Numerical solutions and their superconvergence for weakly singular integral equations with discontinuous coefficients ” . In Mathematical Modelling and Analysis , Edited by: Ciegis , R. Vol. 3 , 104 – 113 . Vilnius : Technika .
  • Kantorovitch , L. V. and Akilov , G. P. 1977 . Functional Analysis , Moscow : Nauka . (in Russian)
  • Pedas , A. and Vainikko , G. 1994 . The smoothness of solutions to nonlinear weakly singular integral equations . Z. Anal. Anwendungen , 13 : 463 – 467 .
  • Tamme , E. 1995 . Two‐grid method for nonlinear multi‐dimensional weakly singular integral equations . J. Integral Equations Appl. , 7 : 99 – 113 .
  • Tamme , E. 1997 . Two‐grid method for the solution of weakly singular integral equations by piecewise polynomial approximation . Proc. Estonian Acad. Sci. Phys. Math. , 46 : 241 – 250 .
  • Uba , P. 1988 . Smoothness of the solution of the weakly singular integral equation with discontinuous coefficient . Proc. Estonian Acad. Sci. Phys. Math. , 37 (2) : 192 – 203 . (in Russian)
  • Vainikko , G. 1993 . Multidimensional weakly singular integral equations , Berlin : Springer Verlag .
  • Vainikko , G. , Pedas , A. and Uba , P. 1984 . Methods for Solving Weakly Singular Integral Equations , Tartu : Univ. of Tartu . (in Russian)
  • This research was supported by the Estonian Science Foundation, grant No. 2999.

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