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Original Articles

An extrapolation procedure for the evaluation of singular integrals

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Pages 251-265 | Received 01 Nov 1981, Published online: 21 Dec 2010

References

  • Davis , P. J. and Rabinowitz , P. 1967 . Numerical Integration , Waltham, MA : Blaisdell .
  • Cohen , A. M. 1980 . Cautious Romberg extrapolation . Intern. J. Computer Math. , 8 : 137 – 147 .
  • Chisholm , J. S. R. , Genz , A. and Rowlands , Glenys E. 1973 . Accelerated convergence of sequences of quadrature approximations . J. Comp. Phys. , 10 : 284 – 307 .
  • Stenger , F. 1973 . Integration formulae based on the trapezoidal formula . J. Inst. Math. Applic. , 12 : 102 – 114 .
  • Squire , W. 1976 . A quadrature method for finite intervals . Int. J. Num. Meth. Engng. , 10 : 708 – 712 .
  • Squire , W. 1979 . A comment on quadrature in the presence of end point singularities . Intern. J. Computer Math. , 7 : 239 – 241 .
  • Harris , C. G. and Evans , W. A. B. 1977 . Extension of numerical quadrature formulae to cater for end point singular behaviour over finite intervals . Intern. J. Computer Math. , 6 : 219 – 227 .
  • Patterson , T. N. L. 1968 . The optimum addition of points to quadrature formulae . Math. Comp. , 22 : 847 – 856 .
  • Clenshaw , C. W. and Curtis , A. R. 1960 . A method for numerical integration on an automatic computer . Numer. Math. , 2 : 197 – 205 .
  • Shanks , D. 1955 . Non-linear transformations of divergent and slowly convergent sequences . J. Math. Phys. , 34 : 1 – 42 .
  • Blakemore , M. , Evans , G. A. and Hyslop , J. 1976 . Comparison of some methods for evaluating infinite range oscillatory integrals . J. Comp. Phys. , 22 : 352 – 376 .
  • Wynn , P. 1956 . On a device for computing the e m (S n ) transformations . Math. Comp. , 10 : 91 – 96 .
  • Levin , D. 1973 . Development of non-linear transformations, for improving convergence of sequences . Intern. J. Computer Math. , 3 : 371 – 388 .

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