Chebyshev wavelet method for hypersingular integrals on circles and its applications

References

• Babuska, I. & Yu, D. H. 1987, “Asymptotically exact a-posteriori error estimator for biquadratic elements”, Finite Elements in Analysis and Design, Vol. 3, pp. 341–354.
   Google Scholar
• Babolian, E. & Fattahzadeh, F. 2007, “Numerical computation method in solving integral equations by using Chebyshev wavelet operational matrix of integration”, Appl. Math. Comput., Vol. 188, pp. 1016–1022.
   Google Scholar
• Chen, Y. Z. 2004, “Hypersingular integral equation method for three-dimensional crack problem in shear mode”, Comm. Numer. Methods Engrg., Vol. 20, pp. 441–454.
   Google Scholar
• Du, Q. K. 2001, “Evaluations of certain hypersingular integrals on interval”, Inter. J. Numer. Methods Engng., Vol. 51, pp. 1195–1210.
   Google Scholar
• Du, Q. K. 2002, “A domain decomposition method based on natural boundary reduction for nonlinear time-dependent exterior wave problems”, Computing, Vol. 68, pp. 111–129.
   Google Scholar
• Ge, Z. X. & Sha, W. 2007, Wavelet analysis theorem and MATLAB application, Electronic-industrial publication, Beijing.
   Google Scholar
• Li, Z. C. & Luo, J. S. 2005, Wavelet analysis and its application, Electronic-industrial publication, Beijing.
   Google Scholar
• Li, J. & Yu, D. H. 2011a, “The Superconvergence of Certain Two-Dimensional Cauchy Principal Value Integrals”, CMES, Vol. 71, No. 4, pp. 331–346.
   Google Scholar
• Li, J. & Yu, D. H. 2011b, “The superconvergence of certain two-dimensional Hilbert singular integrals”, CMES, Vol. 82, No. 4, pp. 233–252.
   Google Scholar
• Li, J., Wu, J. M. & Yu, D. H. 2009, “Generalized extrapolation for computation of hypersingular integrals in boundary element methods”, CMES, Vol. 42, pp. 151–175.
   Google Scholar
• Li, J., Zhang, X. P. & Yu, D. H. 2010, “Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals”, J. Comput. Appl. Math., Vol. 233, pp. 2841–2854.
   Google Scholar
• Liem, C. B., Lii, T. & Shih, T. M. 1995, The Splitting Extrapolation Method, World Scientific, Singapore.
   Google Scholar
• Linz, P. 1985, “On the approximate computation of certain strongly singular integrals”, Computing, Vol. 35, pp. 345–353.
   Google Scholar
• Sun, W. W. & Wu, J. M. 2005, “Newton-Cotes formulae for the numerical evaluation of certain hypersingular integral”, Computing, Vol. 5, pp. 297–309.
   Google Scholar
• Wu, J. M. & Sun, W. W. 2005, “The Superconvergence of the Composite Trapezoidal Rule for Hadamard Finite Part Integrals”, Numer. Math., Vol. 102, No. 2, pp. 343–363.
   Google Scholar
• Wu, J. M. & Sun, W. W. 2008, “The Superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval”, Numer. Math., Vol. 109, No. 1, pp. 143–165.
   Google Scholar
• Wu, J. M., Wang, Y. X. & Li, W. 2008, “Toeplitz-type approximations to the Hadamard integral operator and their applications to electromagnetic cavity problems”, Appl. Numer. Math., Vol. 58, pp. 101–121.
   Google Scholar
• Yu, D. H. 1983, “Numerical solutions of harmonic and biharmonic canonical integral equations in interior or exterior circular domains”, J. Comp. Math., Vol. 1, pp. 52–62.
   Google Scholar
• Yu, D. H. 1993, “The numerical computation of hypersingular integrals and its application in BEM”, Advances in Engineering Software, Vol. 18, pp. 103–109.
   Google Scholar
• Yu, D. H. 1994, “The computation of hypersingular integrals on circle and its error estimates”, Numerical Mathematics, Vol. 12, No. 4, pp. 332–337.
   Google Scholar
• Yu, D. H. 2002, Natural Boundary Integral Method and its Application, Science Press, Kluwer Academic Publishers, Beijing.
   Google Scholar
• Zhang, X. P. & Wu, J. M. 2009, “Superconvergence of the composite Simpson’s rule for a certain finite – Part integral and its applications”, J. Comput. Appl. Math., Vol. 23, pp. 598–613.
   Google Scholar