메뉴 건너뛰기




Volumn 35, Issue 3, 1999, Pages 249-273

Application of nonclassical orthogonal polynomials in particle transport theory

Author keywords

[No Author keywords available]

Indexed keywords

POLYNOMIALS;

EID: 0033353733     PISSN: 01491970     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0149-1970(99)00018-9     Document Type: Article
Times cited : (11)

References (82)
  • 3
    • 0001217979 scopus 로고
    • Discrete-ordinate method of solution of Fokker-Planck equations with nonlinear coefficients
    • Blackmore R. and Shizgal B. (1985) Discrete-ordinate method of solution of Fokker-Planck equations with nonlinear coefficients. Phys. Rev. A 31, 1855.
    • (1985) Phys. Rev. A , vol.31 , pp. 1855
    • Blackmore, R.1    Shizgal, B.2
  • 4
    • 0012070698 scopus 로고
    • Elementary solutions of the transport equation and their applications
    • Case K. M. (1960) Elementary solutions of the transport equation and their applications. Ann. Phys. 9, 1.
    • (1960) Ann. Phys. , vol.9 , pp. 1
    • Case, K.M.1
  • 6
    • 0031232491 scopus 로고    scopus 로고
    • On the solution of Azimuthally dependent transport problems with the ANISN code
    • Chalhoub E. S. and Garcia R. D. M. (1997) On the solution of Azimuthally dependent transport problems with the ANISN code. Ann. Nucl. Energy 24, 1069.
    • (1997) Ann. Nucl. Energy , vol.24 , pp. 1069
    • Chalhoub, E.S.1    Garcia, R.D.M.2
  • 7
    • 0032392569 scopus 로고    scopus 로고
    • A new quadrature scheme for solving Azimuthally dependent transport problems
    • Chalhoub E. S. and Garcia R. D. M. (1998) A new quadrature scheme for solving Azimuthally dependent transport problems. Transp. Theory Stat. Phys. 27, 607.
    • (1998) Transp. Theory Stat. Phys. , vol.27 , pp. 607
    • Chalhoub, E.S.1    Garcia, R.D.M.2
  • 9
    • 0001937414 scopus 로고
    • Sur l'interpolation par la méthode des moindres carrés
    • Chebyshev P. L. (1859) Sur l'interpolation par la méthode des moindres carrés. Mém. Acad. Impér. Sci. St. Pétersbourg (7) 1, 1.
    • (1859) Mém. Acad. Impér. Sci. St. Pétersbourg , vol.1 , Issue.7 , pp. 1
    • Chebyshev, P.L.1
  • 11
    • 84943473262 scopus 로고
    • Über die gaussische quadratur und eine verallgemeinerung derselben
    • Christoffel E. B. (1858) Über die gaussische quadratur und eine verallgemeinerung derselben. J. Reine Angew. Math. 55, 61.
    • (1858) J. Reine Angew. Math. , vol.55 , pp. 61
    • Christoffel, E.B.1
  • 12
    • 0008518813 scopus 로고
    • Sur une classe particulière de fonctions entières et de fractions continues
    • Christoffel E. B. (1877) Sur une classe particulière de fonctions entières et de fractions continues. Ann. Mat. Pura Appl. (2) 8, 1.
    • (1877) Ann. Mat. Pura Appl. , vol.8 , Issue.2 , pp. 1
    • Christoffel, E.B.1
  • 13
    • 84968505704 scopus 로고
    • A note on the summation of Chebyshev series
    • Clenshaw C. W. (1955) A note on the summation of Chebyshev series, Math. Tables Aids Comput. 9, 118.
    • (1955) Math. Tables Aids Comput. , vol.9 , pp. 118
    • Clenshaw, C.W.1
  • 14
    • 0001956676 scopus 로고
    • Mémoire sur l'Approximation des Fonctions de Très-Grands Nombres et sur une Classe Étendue de Développements en Série
    • Darboux G. (1878) Mémoire sur l'Approximation des Fonctions de Très-Grands Nombres et sur une Classe Étendue de Développements en Série. J. Math. Pures Appl. (3) 4, 5.
    • (1878) J. Math. Pures Appl. , vol.4 , Issue.3 , pp. 5
    • Darboux, G.1
  • 20
    • 0000230775 scopus 로고
    • Mechanische Quadraturen mit Positiven Cotesschen Zahlen
    • Fejér L. (1933) Mechanische Quadraturen mit Positiven Cotesschen Zahlen. Math Z. 37, 287.
    • (1933) Math Z. , vol.37 , pp. 287
    • Fejér, L.1
  • 21
    • 0000394782 scopus 로고
    • The Q-R transformation: A unitary analogue to the L-R transformation
    • Francis J. G. F. (1961) The Q-R transformation: A unitary analogue to the L-R transformation. I Comput. J. 4, 265.
    • (1961) I Comput. J. , vol.4 , pp. 265
    • Francis, J.G.F.1
  • 22
    • 0000394779 scopus 로고
    • The Q-R transformation: A unitary analogue to the L-R transformation
    • Francis J. G. F. (1962) The Q-R transformation: A unitary analogue to the L-R transformation. II Comput. J. 4, 332.
    • (1962) II Comput. J. , vol.4 , pp. 332
    • Francis, J.G.F.1
  • 24
    • 84968490637 scopus 로고
    • An implementation of Christoffel's theorem in the theory of Orthogonal polynomials
    • Galant D. (1971) An implementation of Christoffel's theorem in the theory of Orthogonal polynomials. Math. Comp. 25, 111.
    • (1971) Math. Comp. , vol.25 , pp. 111
    • Galant, D.1
  • 26
    • 0033187888 scopus 로고    scopus 로고
    • Improved discrete-ordinates calculations for an approximate model of neutral particle transport in Ducts
    • accepted for publication
    • Garcia R. D. M. and Ono S. (1999) Improved discrete-ordinates calculations for an approximate model of neutral particle transport in Ducts. Nucl. Sci. Eng., accepted for publication.
    • (1999) Nucl. Sci. Eng.
    • Garcia, R.D.M.1    Ono, S.2
  • 27
    • 34250228645 scopus 로고
    • On the dispersion function in particle transport theory
    • Garcia R. D. M. and Siewert C. E. (1982) On the dispersion function in particle transport theory. Z. Angew. Math. Phys. 33, 801.
    • (1982) Z. Angew. Math. Phys. , vol.33 , pp. 801
    • Garcia, R.D.M.1    Siewert, C.E.2
  • 29
    • 0000248782 scopus 로고
    • On computing the Chandrasekhar polynomials in high order and high degree
    • Garcia R. D. M. and Siewert C. E. (1990) On computing the Chandrasekhar polynomials in high order and high degree. J. Quant. Spectrosc. Radiat. Transfer 43, 201.
    • (1990) J. Quant. Spectrosc. Radiat. Transfer , vol.43 , pp. 201
    • Garcia, R.D.M.1    Siewert, C.E.2
  • 32
    • 0002334558 scopus 로고
    • Computational aspects of three-term recurrence relations
    • Gautschi W. (1967) Computational aspects of three-term recurrence relations. SIAM Rev. 9, 24.
    • (1967) SIAM Rev. , vol.9 , pp. 24
    • Gautschi, W.1
  • 33
    • 84968482063 scopus 로고
    • Construction of Gauss-Christoffel quadrature formulas
    • Gautschi W. (1968a) Construction of Gauss-Christoffel quadrature formulas. Math. Comp. 22, 251.
    • (1968) Math. Comp. , vol.22 , pp. 251
    • Gautschi, W.1
  • 34
    • 84945708081 scopus 로고
    • Algorithm 331-Gaussian quadrature formulas
    • Gautschi W. (1968b) Algorithm 331-Gaussian quadrature formulas. Comm. ACM 11, 432.
    • (1968) Comm. ACM , vol.11 , pp. 432
    • Gautschi, W.1
  • 35
    • 0008494990 scopus 로고
    • Questions of numerical condition related to polynomials
    • C. de Boor and G. H. Golub, eds., Academic Press, New York
    • Gautschi W. (1978) Questions of numerical condition related to polynomials. In Recent Advances in Numerical Analysis (C. de Boor and G. H. Golub, eds.), p. 45, Academic Press, New York.
    • (1978) Recent Advances in Numerical Analysis , pp. 45
    • Gautschi, W.1
  • 36
    • 0002459212 scopus 로고
    • On generating Gaussian quadrature rules
    • G. Hämmerlin, ed., Birkhäuser, Basel
    • Gautschi W. (1979) On generating Gaussian quadrature rules. In Numerische Integration (G. Hämmerlin, ed.), p. 147, Birkhäuser, Basel.
    • (1979) Numerische Integration , pp. 147
    • Gautschi, W.1
  • 37
    • 84966208168 scopus 로고
    • Minimal solutions of three-term recurrence relations and Orthogonal polynomials
    • Gautschi W. (1981) Minimal solutions of three-term recurrence relations and Orthogonal polynomials. Math. Comp. 36, 547.
    • (1981) Math. Comp. , vol.36 , pp. 547
    • Gautschi, W.1
  • 38
    • 0001505159 scopus 로고
    • On generating Orthogonal polynomials
    • Gautschi W. (1982a) On generating Orthogonal polynomials. SIAM J. Sci. Stat. Comput. 3, 289.
    • (1982) SIAM J. Sci. Stat. Comput. , vol.3 , pp. 289
    • Gautschi, W.1
  • 39
    • 0001849258 scopus 로고
    • An algorithmic implementation of the generalized Christoffel theorem
    • G. Hämmerlin, ed., Birkhäuser, Basel
    • Gautschi W. (1982b) An algorithmic implementation of the generalized Christoffel theorem. In Numerical Integration (G. Hämmerlin, ed.), p. 89, Birkhäuser, Basel.
    • (1982) Numerical Integration , pp. 89
    • Gautschi, W.1
  • 40
    • 0021569678 scopus 로고
    • On some Orthogonal polynomials of interest in theoretical chemistry
    • Gautschi W. (1984) On some Orthogonal polynomials of interest in theoretical chemistry. BIT 24, 473.
    • (1984) BIT , vol.24 , pp. 473
    • Gautschi, W.1
  • 41
    • 0002888704 scopus 로고
    • Orthogonal polynomials - Constructive theory and applications
    • Gautschi W. (1985) Orthogonal polynomials - Constructive theory and applications. J. Comput. Applied Math. 12&13, 61.
    • (1985) J. Comput. Applied Math. , vol.12-13 , pp. 61
    • Gautschi, W.1
  • 42
    • 0008490343 scopus 로고
    • Computational aspects of Orthogonal polynomials
    • P. Nevai, ed., Kluwer Academic Publishers, Dordrecht, The Netherlands
    • Gautschi W. (1990) Computational aspects of Orthogonal polynomials. In Orthogonal Polynomials: Theory and Practice (P. Nevai, ed.), p. 181, Kluwer Academic Publishers, Dordrecht, The Netherlands.
    • (1990) Orthogonal Polynomials: Theory and Practice , pp. 181
    • Gautschi, W.1
  • 44
    • 0000223746 scopus 로고
    • Calculation of Gauss quadrature rules
    • Golub G. H. and Welsch J. H. (1969) Calculation of Gauss quadrature rules. Math. Comp. 23, 221.
    • (1969) Math. Comp. , vol.23 , pp. 221
    • Golub, G.H.1    Welsch, J.H.2
  • 45
    • 0008437164 scopus 로고
    • Numerical evaluation of the Azimuthally dependent Albedo problem in Slab geometry
    • Hill T. R., Shultis J. K. and Mingle J. O. (1974) Numerical evaluation of the Azimuthally dependent Albedo problem in Slab geometry. J. Comput. Phys. 15, 200.
    • (1974) J. Comput. Phys. , vol.15 , pp. 200
    • Hill, T.R.1    Shultis, J.K.2    Mingle, J.O.3
  • 46
    • 0003378396 scopus 로고
    • Orthogonal polynomials
    • M. Abramowitz and I. A. Stegun, eds., National Bureau of Standards, Washington, D.C.
    • Hochstrasser U. W. (1964) Orthogonal polynomials. In Handbook of Mathematical Functions (M. Abramowitz and I. A. Stegun, eds.), p. 771, National Bureau of Standards, Washington, D.C.
    • (1964) Handbook of Mathematical Functions , pp. 771
    • Hochstrasser, U.W.1
  • 47
    • 0000438447 scopus 로고
    • Orthogonality of a set of polynomials encountered in neutron-transport and radiative-transfer theories
    • Ínönü E. (1970) Orthogonality of a set of polynomials encountered in neutron-transport and radiative-transfer theories. J. Math. Phys. 11, 568.
    • (1970) J. Math. Phys. , vol.11 , pp. 568
    • Ínönü, E.1
  • 48
    • 0021604376 scopus 로고
    • A one-dimensional model for three-dimensional transport in a pipe
    • Larsen E. W. (1984) A one-dimensional model for three-dimensional transport in a pipe. Transp. Theory Stat, Phys. 13, 599.
    • (1984) Transp. Theory Stat, Phys. , vol.13 , pp. 599
    • Larsen, E.W.1
  • 49
    • 0022711322 scopus 로고
    • One-dimensional models for neutral particle transport in Ducts
    • Larsen E. W., Malvagi F. and Pomraning G. C. (1986) One-dimensional models for neutral particle transport in Ducts. Nucl. Sci. Eng. 93, 13.
    • (1986) Nucl. Sci. Eng. , vol.93 , pp. 13
    • Larsen, E.W.1    Malvagi, F.2    Pomraning, G.C.3
  • 51
    • 0001162157 scopus 로고
    • Singular eigenfunction expansions in neutron transport theory
    • McCormick N. J. and Kuščer I. (1973) Singular eigenfunction expansions in neutron transport theory. Adv. Nucl. Sci. Technol. 7, 181.
    • (1973) Adv. Nucl. Sci. Technol. , vol.7 , pp. 181
    • McCormick, N.J.1    Kuščer, I.2
  • 52
    • 0008519529 scopus 로고
    • On the inverse problem of transport theory with Azimuthal dependence
    • McCormick N. J. and Veeder J. A. R. (1978) On the inverse problem of transport theory with Azimuthal dependence. J. Math. Phys. 19, 994.
    • (1978) J. Math. Phys. , vol.19 , pp. 994
    • McCormick, N.J.1    Veeder, J.A.R.2
  • 53
    • 0001049335 scopus 로고
    • Hot-electron zero-field mobility and diffusion in rare-gas moderators
    • McMahon D. R. A. and Shizgal B. (1985) Hot-electron zero-field mobility and diffusion in rare-gas moderators. Phys. Rev. A 31, 1894.
    • (1985) Phys. Rev. A , vol.31 , pp. 1894
    • McMahon, D.R.A.1    Shizgal, B.2
  • 54
    • 0000000708 scopus 로고
    • Neutron transport with Anisotropie scattering
    • Mika J. R. (1961) Neutron transport with Anisotropie scattering. Nucl. Sci. Eng. 11, 415.
    • (1961) Nucl. Sci. Eng. , vol.11 , pp. 415
    • Mika, J.R.1
  • 58
    • 0000705414 scopus 로고
    • An Algorithm for Gaussian quadrature given modified moments
    • Sack R. A. and Donovan A. F. (1972) An Algorithm for Gaussian quadrature given modified moments. Numer. Math. 18, 465.
    • (1972) Numer. Math. , vol.18 , pp. 465
    • Sack, R.A.1    Donovan, A.F.2
  • 59
    • 0008475265 scopus 로고
    • Albedos, Ducts, and Voids
    • N. M. Schaeffer, ed., U.S. Atomic Energy Commission Office of Information Services, Washington, D.C.
    • Selph W. E. (1973) Albedos, Ducts, and Voids. In Reactor Shielding for Nuclear Engineers (N. M. Schaeffer, ed.), p. 313, U.S. Atomic Energy Commission Office of Information Services, Washington, D.C.
    • (1973) Reactor Shielding for Nuclear Engineers , pp. 313
    • Selph, W.E.1
  • 60
    • 0000311177 scopus 로고
    • A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems
    • Shizgal B. (1981a) A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems. J. Comput. Phys. 41, 309.
    • (1981) J. Comput. Phys. , vol.41 , pp. 309
    • Shizgal, B.1
  • 61
    • 0008452432 scopus 로고
    • Nonequilibrium time dependent theory of hot atom reactions. III. Comparison with Estrup-Wolfgang theory
    • Shizgal B. (1981b) Nonequilibrium time dependent theory of hot atom reactions. III. Comparison with Estrup-Wolfgang theory. J. Chem. Phys. 74, 1401.
    • (1981) J. Chem. Phys. , vol.74 , pp. 1401
    • Shizgal, B.1
  • 62
    • 0008494657 scopus 로고
    • Electron thermalization in gases
    • Shizgal B. (1983) Electron thermalization in gases. J. Chem. Phys. 78, 5741.
    • (1983) J. Chem. Phys. , vol.78 , pp. 5741
    • Shizgal, B.1
  • 63
    • 0008523358 scopus 로고
    • Spectral theory and the approach to equilibrium in a plasma
    • Shizgal B. (1992) Spectral theory and the approach to equilibrium in a plasma. Transp. Theory Stat. Phys. 21, 645.
    • (1992) Transp. Theory Stat. Phys. , vol.21 , pp. 645
    • Shizgal, B.1
  • 64
    • 0000131492 scopus 로고
    • Eigenvalues of the Boltzmann collision operator for binary gases: Relaxation of Anisotropie distributions
    • Shizgal B. and Blackmore R. (1983) Eigenvalues of the Boltzmann collision operator for binary gases: Relaxation of Anisotropie distributions. Chem. Phys. 77, 417.
    • (1983) Chem. Phys. , vol.77 , pp. 417
    • Shizgal, B.1    Blackmore, R.2
  • 65
    • 0000523741 scopus 로고
    • A discrete ordinate method of solution of linear boundary value and Eigenvalue problems
    • Shizgal B. and Blackmore R. (1984) A discrete ordinate method of solution of linear boundary value and Eigenvalue problems. J. Comput. Phys. 55, 313.
    • (1984) J. Comput. Phys. , vol.55 , pp. 313
    • Shizgal, B.1    Blackmore, R.2
  • 66
    • 36849113010 scopus 로고
    • Nonequilibrium contribution to the rate of reaction. III. Isothermal multicomponent systems
    • Shizgal B. and Karplus M. (1971) Nonequilibrium contribution to the rate of reaction. III. Isothermal multicomponent systems. J. Chem. Phys. 54, 4357.
    • (1971) J. Chem. Phys. , vol.54 , pp. 4357
    • Shizgal, B.1    Karplus, M.2
  • 67
    • 0001005907 scopus 로고
    • Eigenvalues of the Boltzmann collision operator for binary gases: Mass dependence
    • Shizgal B., Lindenfeld M. J. and Reeves R. (1981) Eigenvalues of the Boltzmann collision operator for binary gases: Mass dependence. Chem. Phys. 56, 249.
    • (1981) Chem. Phys. , vol.56 , pp. 249
    • Shizgal, B.1    Lindenfeld, M.J.2    Reeves, R.3
  • 68
    • 0001276024 scopus 로고
    • Electric distribution functions and thermalization times in inert gas moderators
    • Shizgal B. and McMahon D. R. A. (1984) Electric distribution functions and thermalization times in inert gas moderators. J. Phys. Chem. 88, 4854.
    • (1984) J. Phys. Chem. , vol.88 , pp. 4854
    • Shizgal, B.1    McMahon, D.R.A.2
  • 69
    • 35949016212 scopus 로고
    • Electric field dependence of transient electron transport properties in rare-gas moderators
    • Shizgal B. and McMahon D. R. A. (1985) Electric field dependence of transient electron transport properties in rare-gas moderators. Phys. Rev. A 32, 3669.
    • (1985) Phys. Rev. A , vol.32 , pp. 3669
    • Shizgal, B.1    McMahon, D.R.A.2
  • 71
    • 0018429993 scopus 로고
    • N method in neutron-transport theory. Part I: Theory and applications
    • N method in neutron-transport theory. Part I: Theory and applications. Nucl. Sci. Eng. 69, 156.
    • (1979) Nucl. Sci. Eng. , vol.69 , pp. 156
    • Siewert, C.E.1    Benoist, P.2
  • 75
    • 0008519530 scopus 로고
    • Quelques Recherches sur la Théorie des Quadratures Dites Mécaniques
    • Stieltjes T. J. (1884) Quelques Recherches sur la Théorie des Quadratures Dites Mécaniques. Ann. Sci. ÉCole Norm. Sup. (3) 1, 409.
    • (1884) Ann. Sci. École Norm. Sup. , vol.1 , Issue.3 , pp. 409
    • Stieltjes, T.J.1
  • 77
    • 0004073954 scopus 로고
    • American Mathematical Society, Providence, R.I.
    • Szegö G. (1939) Orthogonal Polynomials, American Mathematical Society, Providence, R.I.
    • (1939) Orthogonal Polynomials
    • Szegö, G.1
  • 78
    • 0008494658 scopus 로고
    • Relation between polynomials Orthogonal with different weights
    • Uvarov V. B. (1959) Relation between polynomials Orthogonal with different weights. Dokl. Akad. Nauk USSR 126, 33.
    • (1959) Dokl. Akad. Nauk USSR , vol.126 , pp. 33
    • Uvarov, V.B.1
  • 79
    • 0001904553 scopus 로고
    • The connection between systems of polynomials that are Orthogonal with respect to different distribution functions
    • Uvarov V. B. (1969) The connection between systems of polynomials that are Orthogonal with respect to different distribution functions. U.S.S.R. Computational Math. and Phys. 9, 25.
    • (1969) U.S.S.R. Computational Math. and Phys. , vol.9 , pp. 25
    • Uvarov, V.B.1
  • 80
    • 0000955005 scopus 로고
    • Modified moments and Gaussian quadrature
    • Wheeler J. C. (1974) Modified moments and Gaussian quadrature. Rocky Mountain J. Math. 4, 287.
    • (1974) Rocky Mountain J. Math. , vol.4 , pp. 287
    • Wheeler, J.C.1
  • 81
    • 0008525906 scopus 로고
    • Modified moments and continued fraction coefficients for the Diatomic linear chain
    • Wheeler J. C. (1984) Modified moments and continued fraction coefficients for the Diatomic linear chain. J. Chem. Phys. 80, 472.
    • (1984) J. Chem. Phys. , vol.80 , pp. 472
    • Wheeler, J.C.1
  • 82
    • 34250920729 scopus 로고
    • Über ebene Diffusionsprobleme
    • Wick, G. C. (1943) Über ebene Diffusionsprobleme. Z. Phys. 121, 702.
    • (1943) Z. Phys. , vol.121 , pp. 702
    • Wick, G.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.