메뉴 건너뛰기




Volumn 132, Issue 1-2, 2000, Pages 142-165

Adaptive contour code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their derivatives

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; FORTRAN (PROGRAMMING LANGUAGE); INTEGRAL EQUATIONS; INTEGRATION; NUMERICAL ANALYSIS;

EID: 0034667286     PISSN: 00104655     EISSN: None     Source Type: None    
DOI: 10.1016/S0010-4655(00)00126-0     Document Type: Article
Times cited : (27)

References (53)
  • 1
    • 0007031855 scopus 로고
    • Practical methods for the uniform asymptotic evaluation of oscillating integrals with several coalescing saddle points
    • R. Wong (Ed.) Dekker, New York
    • J.N.L. Connor, Practical methods for the uniform asymptotic evaluation of oscillating integrals with several coalescing saddle points, in: Asymptotic and Computational Analysis, Conference in Honor of Frank W.J. Olver's 65th Birthday, R. Wong (Ed.) (Dekker, New York, 1990) pp. 137-173.
    • (1990) Asymptotic and Computational Analysis, Conference in Honor of Frank W.J. Olver's 65th Birthday , pp. 137-173
    • Connor, J.N.L.1
  • 6
    • 84975641603 scopus 로고
    • Geometrical and catastrophe optics methods in scattering
    • P.L. Marston, Geometrical and catastrophe optics methods in scattering, Phys. Acoustics 21 (1992) 1-234.
    • (1992) Phys. Acoustics , vol.21 , pp. 1-234
    • Marston, P.L.1
  • 9
    • 11744251442 scopus 로고
    • Semiclassical theory of molecular collisions: Three nearly coincident classical trajectories
    • J.N.L. Connor, Semiclassical theory of molecular collisions: Three nearly coincident classical trajectories, Mol. Phys. 26 (1973) 1217-1231.
    • (1973) Mol. Phys. , vol.26 , pp. 1217-1231
    • Connor, J.N.L.1
  • 10
    • 0000332371 scopus 로고
    • Semiclassical theory of molecular collisions. Many nearly coincident classical trajectories
    • J.N.L. Connor, Semiclassical theory of molecular collisions. Many nearly coincident classical trajectories, Mol. Phys. 27 (1974) 853-866.
    • (1974) Mol. Phys. , vol.27 , pp. 853-866
    • Connor, J.N.L.1
  • 11
    • 84947151907 scopus 로고
    • Catastrophes and molecular collisions
    • J.N.L. Connor, Catastrophes and molecular collisions, Mol. Phys. 31 (1976) 33-55.
    • (1976) Mol. Phys. , vol.31 , pp. 33-55
    • Connor, J.N.L.1
  • 14
    • 0007032820 scopus 로고
    • Uniform asymptotic expansions of integrals: A selection of problems
    • N.M. Temme, Uniform asymptotic expansions of integrals: A selection of problems, J. Comput. Appl. Math. 65 (1995) 395-417.
    • (1995) J. Comput. Appl. Math. , vol.65 , pp. 395-417
    • Temme, N.M.1
  • 15
    • 0000603470 scopus 로고
    • On certain definite integrals considered by Airy and Stokes
    • [reprinted in: Collected Papers of G.H. Hardy, Vol. 4, edited by a Committee appointed by The London Mathematical Society (Clarendon, Oxford, 1969) pp. 460-474]
    • G.H. Hardy, On certain definite integrals considered by Airy and Stokes, Quart. J. 41 (1910) 226-240 [reprinted in: Collected Papers of G.H. Hardy, Vol. 4, edited by a Committee appointed by The London Mathematical Society (Clarendon, Oxford, 1969) pp. 460-474]
    • (1910) Quart. J. , vol.41 , pp. 226-240
    • Hardy, G.H.1
  • 16
    • 0001789466 scopus 로고
    • Normal'nye formy funktsiy v okrestnosti vyrozhdennykh kriticheskikh tochek
    • V.I. Arnol'd, Normal'nye formy funktsiy v okrestnosti vyrozhdennykh kriticheskikh tochek (Normal forms of functions in neighborhoods of degenerate critical points), Usp. Mat. Nauk. 29 (2) (1974) 11-49. [English translation: Russ. Math. Surv. 29 (2) (1974) 10-50; V.I. Arnold, Singularity Theory: Selected Papers (Cambridge University Press, Cambridge, 1981) pp. 91-131.]
    • (1974) Usp. Mat. Nauk. , vol.29 , Issue.2 , pp. 11-49
    • Arnol'd, V.I.1
  • 17
    • 0007083924 scopus 로고
    • V.I. Arnol'd, Normal'nye formy funktsiy v okrestnosti vyrozhdennykh kriticheskikh tochek (Normal forms of functions in neighborhoods of degenerate critical points), Usp. Mat. Nauk. 29 (2) (1974) 11-49. [English translation: Russ. Math. Surv. 29 (2) (1974) 10-50; V.I. Arnold, Singularity Theory: Selected Papers (Cambridge University Press, Cambridge, 1981) pp. 91-131.]
    • (1974) Russ. Math. Surv. , vol.29 , Issue.2 , pp. 10-50
  • 18
    • 0003774868 scopus 로고
    • Cambridge University Press, Cambridge
    • V.I. Arnol'd, Normal'nye formy funktsiy v okrestnosti vyrozhdennykh kriticheskikh tochek (Normal forms of functions in neighborhoods of degenerate critical points), Usp. Mat. Nauk. 29 (2) (1974) 11-49. [English translation: Russ. Math. Surv. 29 (2) (1974) 10-50; V.I. Arnold, Singularity Theory: Selected Papers (Cambridge University Press, Cambridge, 1981) pp. 91-131.]
    • (1981) Singularity Theory: Selected Papers , pp. 91-131
    • Arnold, V.I.1
  • 20
    • 36749111864 scopus 로고
    • Theory of cusped rainbows in elastic scattering: Uniform semiclassical calculations using Pearcey's integral
    • J.N.L. Connor, D. Farrelly, Theory of cusped rainbows in elastic scattering: Uniform semiclassical calculations using Pearcey's integral, J. Chem. Phys. 75 (1981) 2831-2846.
    • (1981) J. Chem. Phys. , vol.75 , pp. 2831-2846
    • Connor, J.N.L.1    Farrelly, D.2
  • 21
    • 0007029450 scopus 로고
    • Fold and cusp catastrophe structures in rotational rainbow scattering
    • F. Wolf, H.J. Korsch, Fold and cusp catastrophe structures in rotational rainbow scattering, J. Chem. Phys. 81 (1984) 3127-3136.
    • (1984) J. Chem. Phys. , vol.81 , pp. 3127-3136
    • Wolf, F.1    Korsch, H.J.2
  • 23
    • 0007117045 scopus 로고
    • The uniform asymptotic swallowtail approximation: Practical methods for oscillating integrals with four coalescing saddle points
    • J.N.L. Connor, P.R. Curtis, D. Farrelly, The uniform asymptotic swallowtail approximation: Practical methods for oscillating integrals with four coalescing saddle points, J. Phys. A 17 (1984) 283-310.
    • (1984) J. Phys. A , vol.17 , pp. 283-310
    • Connor, J.N.L.1    Curtis, P.R.2    Farrelly, D.3
  • 24
    • 25044475613 scopus 로고
    • Molecular collisions and cusp catastrophes: Three methods for the calculation of Pearcey's integral and its derivatives
    • J.N.L. Connor, D. Farrelly, Molecular collisions and cusp catastrophes: Three methods for the calculation of Pearcey's integral and its derivatives, Chem. Phys. Lett. 81 (1981) 306-310.
    • (1981) Chem. Phys. Lett. , vol.81 , pp. 306-310
    • Connor, J.N.L.1    Farrelly, D.2
  • 25
    • 0000728656 scopus 로고
    • A differential equation method for the numerical evaluation of the Airy, Pearcey and swallowtail canonical integrals and their derivatives
    • J.N.L. Connor, P.R. Curtis, D. Farrelly, A differential equation method for the numerical evaluation of the Airy, Pearcey and swallowtail canonical integrals and their derivatives, Mol. Phys. 48 (1983) 1305-1330.
    • (1983) Mol. Phys. , vol.48 , pp. 1305-1330
    • Connor, J.N.L.1    Curtis, P.R.2    Farrelly, D.3
  • 26
    • 0007134267 scopus 로고
    • Differential equations for the cuspoid canonical integrals
    • J.N.L. Connor, P.R. Curtis, Differential equations for the cuspoid canonical integrals, J. Math. Phys. 25 (1984) 2895-2902.
    • (1984) J. Math. Phys. , vol.25 , pp. 2895-2902
    • Connor, J.N.L.1    Curtis, P.R.2
  • 30
    • 0007031862 scopus 로고
    • Comment on "comparison of some methods for evaluating infinite range oscillatory integrals"
    • K.B. Winterbon, Comment on "comparison of some methods for evaluating infinite range oscillatory integrals", J. Comput. Phys. 26 (1978) 447-448.
    • (1978) J. Comput. Phys. , vol.26 , pp. 447-448
    • Winterbon, K.B.1
  • 31
    • 0007080831 scopus 로고
    • Numerical evaluation of a class of integrals by integrating along a string of saddle points
    • R. Lugannani, S.O. Rice, Numerical evaluation of a class of integrals by integrating along a string of saddle points, J. Comput. Phys. 39 (1981) 473-480.
    • (1981) J. Comput. Phys. , vol.39 , pp. 473-480
    • Lugannani, R.1    Rice, S.O.2
  • 32
    • 0031677132 scopus 로고    scopus 로고
    • The evaluation of infinite range oscillatory integrals using optimal contours in the complex plane
    • G.A. Evans, K.C. Chung, The evaluation of infinite range oscillatory integrals using optimal contours in the complex plane, Int. J. Comput. Math. 66 (1998) 39-52.
    • (1998) Int. J. Comput. Math. , vol.66 , pp. 39-52
    • Evans, G.A.1    Chung, K.C.2
  • 33
    • 85031567885 scopus 로고    scopus 로고
    • Partial wave integrals
    • R.J. Allan, M.F. Guest, A.D. Simpson, D.S. Henty, D.A. Nicole (Eds.) Kluwer Academic, New York
    • J. Rasch, C.T. Whelan, Partial wave integrals, in High Performance Computing, R.J. Allan, M.F. Guest, A.D. Simpson, D.S. Henty, D.A. Nicole (Eds.) (Kluwer Academic, New York, 1999) pp. 301-305.
    • (1999) High Performance Computing , pp. 301-305
    • Rasch, J.1    Whelan, C.T.2
  • 34
    • 0007022570 scopus 로고
    • subroutine D01AKF NAG, Oxford
    • Numerical Algorithms Group, FORTRAN Library Manual, Mark 16, Vol. 1, subroutine D01AKF (NAG, Oxford, 1993).
    • (1993) FORTRAN Library Manual, Mark 16 , vol.1
  • 36
    • 84976762558 scopus 로고
    • Local versus global strategies for adaptive quadrature
    • M.A. Malcolm, R.B. Simpson, Local versus global strategies for adaptive quadrature, ACM Trans. Math. Software 1 (1975) 129-146.
    • (1975) ACM Trans. Math. Software , vol.1 , pp. 129-146
    • Malcolm, M.A.1    Simpson, R.B.2
  • 37
    • 0007029452 scopus 로고
    • A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: Application to Pearcey's integral and its derivatives
    • J.N.L. Connor, P.R. Curtis, A method for the numerical evaluation of the oscillatory integrals associated with the cuspoid catastrophes: Application to Pearcey's integral and its derivatives, J. Phys. A 15 (1982) 1179-1190.
    • (1982) J. Phys. A , vol.15 , pp. 1179-1190
    • Connor, J.N.L.1    Curtis, P.R.2
  • 40
    • 0007031868 scopus 로고
    • Chislennye melody pascheta spetsial'nykh funktsiy volnovykh katastrof
    • E.B. Ipatov, D.S. Lukin, E.A. Palkin, Chislennye melody pascheta spetsial'nykh funktsiy volnovykh katastrof (Numerical methods of computing special functions of wave catastrophes), Zh. Vychisl. Mat. Mat. Fiz. 25 (1985) 224-236. [English translation: USSR Comput. Math. Math. Phys. 25 (1985) 144-153. ]
    • (1985) Zh. Vychisl. Mat. Mat. Fiz. , vol.25 , pp. 224-236
    • Ipatov, E.B.1    Lukin, D.S.2    Palkin, E.A.3
  • 41
    • 0007032526 scopus 로고
    • E.B. Ipatov, D.S. Lukin, E.A. Palkin, Chislennye melody pascheta spetsial'nykh funktsiy volnovykh katastrof (Numerical methods of computing special functions of wave catastrophes), Zh. Vychisl. Mat. Mat. Fiz. 25 (1985) 224-236. [English translation: USSR Comput. Math. Math. Phys. 25 (1985) 144-153.]
    • (1985) USSR Comput. Math. Math. Phys. , vol.25 , pp. 144-153
  • 43
    • 84950658895 scopus 로고
    • Evaluation of the field near a cusp of a caustic
    • J.J. Stamnes, B. Spjelkavic, Evaluation of the field near a cusp of a caustic, Optica Acta 30 (1983) 1331-1358.
    • (1983) Optica Acta , vol.30 , pp. 1331-1358
    • Stamnes, J.J.1    Spjelkavic, B.2
  • 45
    • 0141431556 scopus 로고
    • Rays, wavefronts and phase: A picture book of cusps
    • The Hague/Scheveningen, November 19-22, H. Blok, H.A. Ferweda, H.K. Kuiken (Eds.) North-Holland, Amsterdam
    • M. Berry, Rays, wavefronts and phase: A picture book of cusps, in: Huygens' Principle, 1690-1990, Theory and Applications, Proc. Internat. Symposium, The Hague/Scheveningen, November 19-22, 1990, H. Blok, H.A. Ferweda, H.K. Kuiken (Eds.) (North-Holland, Amsterdam, 1992) pp. 97-11 1.
    • (1990) Huygens' Principle, 1690-1990, Theory and Applications, Proc. Internat. Symposium , pp. 97-111
    • Berry, M.1
  • 47
    • 0001342813 scopus 로고
    • Diffraction of pulses in the vicinity of simple caustics and caustic cusps
    • A. Hanyga, M. Seredyńska, Diffraction of pulses in the vicinity of simple caustics and caustic cusps, Wave Motion 14 (1991) 101-121.
    • (1991) Wave Motion , vol.14 , pp. 101-121
    • Hanyga, A.1    Seredyńska, M.2
  • 49
    • 0002341808 scopus 로고
    • The asymptotic behaviour of Pearcey's integral for complex variables
    • R.B. Paris, The asymptotic behaviour of Pearcey's integral for complex variables, Proc. Roy. Soc. London A 432 (1991) 391-426.
    • (1991) Proc. Roy. Soc. London A , vol.432 , pp. 391-426
    • Paris, R.B.1
  • 50
    • 21344494075 scopus 로고
    • A generalization of Pearcey's integral
    • R.B. Paris, A generalization of Pearcey's integral, SIAM J. Math. Anal. 25 (1994) 630-645.
    • (1994) SIAM J. Math. Anal. , vol.25 , pp. 630-645
    • Paris, R.B.1
  • 51
    • 0002327308 scopus 로고
    • Asymptotic evaluation of the Pearcey integral near the caustic
    • D. Kaminski, Asymptotic evaluation of the Pearcey integral near the caustic, SIAM J. Math. Anal. 20 (1989) 987-1005.
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 987-1005
    • Kaminski, D.1
  • 52
    • 0032627884 scopus 로고    scopus 로고
    • On the zeroes of the Pearcey integral
    • D. Kaminski, R.B. Paris, On the zeroes of the Pearcey integral, J. Comput. Appl. Math. 107 (1999) 31-52.
    • (1999) J. Comput. Appl. Math. , vol.107 , pp. 31-52
    • Kaminski, D.1    Paris, R.B.2
  • 53
    • 0007022576 scopus 로고
    • Asymptotics of the swallowtail integral near the cusp of the caustic
    • D. Kaminski, Asymptotics of the swallowtail integral near the cusp of the caustic, SIAM J. Math. Anal. 23 (1994) 262-285.
    • (1994) SIAM J. Math. Anal. , vol.23 , pp. 262-285
    • Kaminski, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.