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Section B

Numerical solution and spectrum of boundary-domain integral equation for the Neumann BVP with a variable coefficient

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Pages 1488-1503 | Received 02 Nov 2011, Accepted 06 Mar 2012, Published online: 30 Apr 2012

References

  • Beer , G. 2001 . Programming the Boundary Element Method , Chichester : John Wiley & Sons .
  • Chkadua , O. , Mikhailov , S. E. and Natroshvili , D. 2009 . Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient, I: Equivalence and invertibility . J. Integral Equ. Appl. , 21 : 499 – 543 .
  • Chkadua , O. , Mikhailov , S. E. and Natroshvili , D. 2009 . Analysis of some localized boundary-domain integral equations . J. Integral Equ. Appl. , 21 : 405 – 445 .
  • Chkadua , O. , Mikhailov , S. E. and Natroshvili , D. 2011 . Analysis of segregated boundary-domain integral equations for variable-coefficient problems with cracks . Numer. Methods Partial Differential Equ. , 27 : 121 – 140 .
  • Goursat , E. 1964 . A Course in Mathematical Analysis , Vol. 3 , Boston , MA : Part 2: Integral Equations, Calculus of Variations, Ginn .
  • Kantorovich , L. V. and Krylov , V. I. 1964 . Approximate Methods of Higher Analysis , New York : Wiley Interscience Publishers .
  • Kublanovskaya , V. N. 1959 . Application of analytic continuation by change of variables in numerical analysis . Proc. Math. Inst. Acad. Sci. USSR , 53 : 145 – 185 .
  • Mikhailov , S. E. 1983 . On an integral equation of some boundary value problems for harmonic functions in plane multiply connected domains with nonregular boundary . Matematicheskii Sbornik , 121 : 533 – 544 . (English Translation: Mathematics of the USSR Sbornik 49 (1984), pp. 525–536).
  • Mikhailov , S. E. 1999 . Finite-dimensional perturbations of linear operators and some applications to boundary integral equations . Eng. Anal. Bound. Elem. , 23 : 805 – 813 .
  • Mikhailov , S. E. 2002 . Localized boundary-domain integral formulations for problems with variable coefficients . Eng. Anal. Bound. Elem. , 26 : 681 – 690 .
  • Mikhailov , S. E. 2005 . Localized direct boundary-domain integro-differential formulations for scalar nonlinear boundary-value problems with variable coefficients . J. Eng. Math. , 51 : 283 – 302 .
  • Mikhailov , S. E. 2006 . Analysis of united boundary-domain integro-differential and integral equations for a mixed BVP with variable coefficient . Math. Methods Appl. Sci. , 29 : 715 – 739 .
  • Mikhailov , S. E. and Mohamed , N. A. Iterative solution of boundary-domain integral equation for BVP with variable coefficient . Proceedings of the 8th UK Conference on Boundary Integral Methods , Edited by: Lesnic , D. pp. 127 – 134 . Leeds : Leeds University Press .
  • Mikhailov , S. E. and Nakhova , I. S. 2005 . Mesh-based numerical implementation of the localized boundary-domain integral equation method to a variable-coefficient Neumann problem . J. Eng. Math. , 51 : 251 – 259 .
  • Mikhlin , S. G. 1957 . Integral Equations and Application to Certain Problems in Mechanics , New York : Pergamon Press .
  • Steinbach , O. and Wendland , W. 2001 . On C. Neumann's method for second-order elliptic systems in domains with non-smooth boundaries . J. Math. Anal. Appl. , 262 : 733 – 748 .

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