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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 48, 1983 - Issue 6
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Original Articles

A differential equation method for the numerical evaluation of the Airy, Pearcey and swallowtail canonical integrals and their derivatives

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Pages 1305-1330 | Received 19 Aug 1982, Accepted 09 Nov 1982, Published online: 22 Aug 2006

References

  • Child , M.S. , ed. Semiclassical Methods in Molecular Scattering and Spectroscopy . Proceedings of the NATO Advanced Study Institute held in Cambridge . September 1979 , England. Reidel .
  • Chester , C. , Friedman , B. and Ursell , F. 1957 . Proc. Camb. phil. Soc. math. phys. Sci. , 53 : 599 – 599 . Friedman, B., 1959, J. Soc. ind. appl. Math., 7, 280.
  • Bleistein , N. 1967 . J. Math. Mech. , 17 : 533 – 533 .
  • Rice , S.O. 1968 . Bell Syst. tech. J. , 47 : 1970 – 1970 .
  • Ursell , F. 1972 . Proc. Camb. phil. Soc. math. phys. Sci. , 72 : 49 – 49 .
  • Connor , J.N.L. 1976 . Molec. Phys. , 31 : 33 – 33 .
  • Connor , J.N.L. and Marcus , R.A. 1971 . J. chem. Phys. , 55 : 5636 – 5636 .
  • Connor , J.N.L. Semiclassical Methods in Molecular Scattering and Spectroscopy . Proceedings of the NATO Advanced Study Institute held in Cambridge . September 1979 , England. Edited by: Child , M.S. pp. 45 – 107 . Reidel .
  • Thom , R. 1975 . Structural Stability and Morphogenesis. An Outline of a General Theory of Models , Edited by: Fowler , D.H. Benjamin . translated from the French edition, as updated by the author with a foreword by C. H. Waddington
  • Poston , T. and Stewart , I. 1978 . Catastrophe Theory and its Applications , Pitman .
  • Gilmore , R. 1981 . Catastrophe Theory for Scientists and Engineers , Wiley .
  • Miller , J.C.P. 1971 . The Airy Integral, Giving Tables of Solutions of the Differential Equation y″ = xy , Cambridge : the University Press . British Association for the Advancement of Science, Mathematical Tables, Part-volume B, published for the Royal Society at
  • Antosiewicz , H.A. 1965 . Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables , Edited by: Abramowitz , M. and Stegun , I.A. Dover . Chap. 10
  • Brillouin , L. 1916 . Annls scient. Éc. norm. sup., Paris, Ser. 3 , 33 : 17 – 17 .
  • Pearcey , T. 1946 . Lond. Edinb. Dubl. Phil. Mag. , 37 : 311 – 311 .
  • Pearcey , T. 1963 . The Effect of Aberrations upon the Optical Focus , Edited by: Pearcey , T. and Hill , G.W. 1 – 40 . Melbourne, , Australia : Commonwealth Scientific and Industrial Research Organization .
  • Connor , J.N.L. 1973 . Molec. Phys. , 26 : 1217 – 1217 .
  • Connor , J.N.L. and Farrelly , D. 1981 . J. chem. Phys. , 75 : 2831 – 2831 . On p. 2837, 2nd column, line 27 for ‘Fig. 6’ read ‘Ref. 6’.
  • Connor , J.N.L. and Farrelly , D. 1981 . Chem. Phys. Lett. , 81 : 306 – 306 .
  • Connor , J.N.L. and Curtis , P.R. 1982 . J. Phys. A , 15 : 1179 – 1179 .
  • Connor , J.N.L. 1974 . Molec. Phys. , 27 : 853 – 853 . On p. 861, lines 25 and 26, the words ‘even’ and ‘odd’ should be interchanged.
  • Pearcey , T. and Hill , G.W. 1963 . The Effect of Aberrations upon the Optical Focus , Edited by: Pearcey , T. and Hill , G.W. 41 – 70 . Melbourne, , Australia : Commonwealth Scientific and Industrial Research Organization .
  • Connor , J.N.L. , Edge , C.J. and Laganà , A. 1982 . Molec. Phys. , 46 : 1231 – 1231 .
  • Hardy , G.H. 1910 . Q. Jl. , 41 : 226 – 226 . reprinted in: 1969, Collected Papers of G. H. Hardy, Vol. IV, edited by a Committee appointed by The London Mathematical Society (Clarendon), p. 460.
  • Watson , G.N. 1944 . Theory of Bessel Functions , 2nd edition , 188 – 190 . Cambridge University Press .
  • Schulten , Z. , Anderson , D.G.M. and Gordon , R.G. 1979 . J. comput. Phys. , 31 : 60 – 60 .
  • Barnett , A.R. 1981 . Comput. Phys. Commun. , 21 : 297 – 297 .
  • Razaz , M. and Schonfelder , J.L. 1981 . ACM Trans. Math. Software , 7 : 404 – 404 .
  • Hartree , D.R. , Michel , J.G.L. and Nicholson , P. Meteorological Factors in Radio-wave Propagation . Report of a Conference held on 8th April 1946 at The Royal Institution . London. pp. 127 – 127 . The Physical Society and The Royal Meteorological Society (Physical Society) .
  • Hartree , D.R. 1949 . “ Differential Analyser ” . In Permanent Records of Research and Development, No. 17.502 , 2.53.1 – 2.53.1 . London : Ministry of Supply .
  • Johnson , W.W. 1889 . A Treatise on Ordinary and Partial Differential Equations , Macmillan . § 129
  • Messiah , A. 1961 . Quantum Mechanics , Edited by: Temmer , G.M. Vol. I , North-Holland . Chap. III
  • 1978 . Numerical Algorithms Group, Gortran Library Manual Mark 7, subroutine D02CBF
  • Hall , G. and Watt , J.M. , eds. 1976 . Modern Numerical Methods for Ordinary Differential Equations Oxford
  • Connor , J.N.L. , Curtis , P.R. and Farrelly , D. The uniform asymptotic swallow-tail approximation: practical methods for oscillating integrals with four coalescing saddle points (to be published)
  • Wright , F.J. 1977 . Ph.D. thesis , England : University of Bristol .
  • Pope , N.A. 1981 . M.A. thesis , U.S.A. : University of South Florida .
  • Berry , M.V. , Nye , F.J. and Wright , F.J. 1979 . Phil. Trans. R. Soc. A , 291 : 453 – 453 .

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