The evaluation of infinite range oscillatory integrals using optimal contours in the complex plane

References

• Copson , E. T. 1972 . An introduction to the theory of functions of a complex variable , Oxford University Press .
   Google Scholar
• Evans , G. A. 1992 . The higher order use of the trapezoidal rule in numerical quadrature . Int. J. Math. Educ. Sci. Technol. , 23 ( 4 ) : 525 – 536 .
   Google Scholar
• Evans , G. A. , Forbes , R. C. and Hyslop , J. 1987 . Solution of non-linear Fredholm integral equations by a variational approach . Int. J. Comp. Math. , 22 ( 2 ) : 149 – 159 .
   Web of Science ®Google Scholar
• Squire , W. 1976 . A quadrature method for finite intervals . Int. J. Numer. Methods Eng. , 10 : 708 – 712 .
   Web of Science ®Google Scholar
• Iri M. Moriguti S. Takasawa y. n a certain quadrature formula, Kokyuroku R. I. M. S. Kyoto University, No. 1970 82 118
   Google Scholar
• Aihie , V. U. and Evans , G. A. 1989 . Variable transformation methods and their use in general and singular quadratures . Int. J. Comp. Math. , 27 ( 2 ) : 91 – 101 .
   Web of Science ®Google Scholar
• Alaylioglu , A. , Evans , G. A. and Hyslop , J. 1975 . Automatic generation of quadrature formulae for oscillatory integrals . C. J. , 18 ( 2 ) : 173 – 176 .
   Web of Science ®Google Scholar
• Patterson , T. N. L. 1976 . On high precision methods for the evaluation of Fourier integrals with finite and infinite limits . Numer. Math. , 23 : 411 – 412 .
   Google Scholar
• Alaylioglu , A. , Evans , G. A. and Hyslop , J. 1976 . The use of Chebyshev series for the evaluation of oscillatory integrals . C. J. , 19 ( 3 ) : 258 – 267 .
   Web of Science ®Google Scholar
• Shanks , D. 1955 . Nonlinear transformations of divergent and slowly convergent sequences . J. Math, and Phys. , 34 : 1 – 42 .
   Web of Science ®Google Scholar
• Levin , D. 1982 . Procedure for computing one and two dimensional integrals of functions with rapid irregular oscillations . Math. Comp. , 38 ( 158 ) : 531 – 538 .
   Web of Science ®Google Scholar
• Alaylioglu , A. , Evans , G. A. and Hyslop , J. 1973 . The evaluation of oscillatory integrals with infinite limits . J. Comp. Phys. , 13 : 433 – 438 .
   Web of Science ®Google Scholar
• Piessens , R. and Haegemans , A. 1973 . Numerical calculation of Fourier transform integrals . Electron. Lett. , 9 ( 5 ) : 108 – 109 .
   Web of Science ®Google Scholar
• Hurwitz , H. and Zweifel , P. F. 1956 . Numerical quadrature of Fourier transform integrals . M. T. A. C , 10 : 89 – 90 .
   Google Scholar
• Boris , J. P. and Oran , E. S. 1975 . Numerical evaluation of oscillatory integrals such as the modified Bessel function K iζ (x) . J. Comp. Phys. , 17 : 425 – 433 .
   Google Scholar
• Pantis , G. 1975 . The evaluation of integrals with oscillatory integrands . J. Comp. Phys. , 17 : 229 – 233 .
   Web of Science ®Google Scholar
• Filon , L. N. G. 1928 . On a quadrature formula for trigonometric integrals . Proc. Roy. Soc. Edinburgh , 49 : 38 – 47 .
   Google Scholar
• Clenshaw , C. W. and Curtis , A. R. 1960 . A method for numerical integration on an automatic computer . Numer. Math. , 12 : 197 – 205 .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar