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Original Articles

Calculating the Discrete Spectrum of the Transport Operator with Arbitrary Order Anisotropic Scattering

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Pages 179-197 | Received 15 Oct 2005, Accepted 23 Jun 2006, Published online: 04 Dec 2010

References

  • Bauer , F. and Stoer , J. 1962 . Algorithm 105: Newton Maehly . Comm. ACM , 5 : 387 – 388 .
  • Boyd , J. 2002 . Computing zeros on a real interval through Chebyshev expansion and polynomial rootfinding . SIAM J. Numer. Anal. , 40 ( 5 ) : 1666 – 1682 .
  • Case , K. 1974 . Scattering theory, orthogonal polynomials, and the transport equation . J. Math. Phys. , 15 ( 7 ) : 974 – 983 .
  • Case , K. and Zweifel , P. 1967 . Linear Transport Theory Addison‐Wesley .
  • Chihara , T. and Nevai , P. 1982 . Orthogonal polynomials and measures with finitely many point masses . J. Approx. Theory , 35 : 370 – 380 .
  • Freud , G. 1986 . On the greatest zero of an orthogonal polynomial . J. Approx. Theory , 46 : 16 – 24 .
  • Garcia , R. and Siewert , C. 1989 . On discrete spectrum calculations in radiative transfer . J. Quant. Spectrosc. Radiat. Transf. , 42 ( 5 ) : 385 – 394 .
  • Geronimo , J. and Case , K. 1980 . Scattering theory and polynomials orthogonal on the real line . Trans. AMS , 258 ( 2 ) : 467 – 494 .
  • Golub , G. and Van Loan , C. 1996 . Matrix Computations , 2nd edn. John Hopkins University Press .
  • Henyey , L. and Greenstein , J. 1941 . Diffuse radiation in the galaxy . Astrophys. J. , 93 : 70 – 83 .
  • Higham , N. 2002 . Accuracy and Stability of Numerical Algorithms , 2nd edn. SIAM .
  • Inönü , E. 1970 . Orthogonality of a set of polynomials encountered in neutron‐transport and radiative‐transfer theories . J. Math. Phys. , 11 ( 2 ) : 568 – 577 .
  • Jenkins , M. 1975 . Algorithm 493: Zeros of a real polynomial . ACM Trans. Math. Software , 1 ( 2 ) : 178 – 189 .
  • Jenkins , M. and Traub , J. 1970 . A three‐stage algorithm for real polynomials using quadratic iteration . SIAM J. Numer. Anal. , 7 : 545 – 566 .
  • Kaper , H. , Shultis , J. and Veninga , J. 1970 . Numerical evaluation of the slab albedo solution in one‐speed anisotropic transport theory . J. Comput. Phys. , 6 : 288 – 313 .
  • Magnus , W. , Oberhettinger , F. and Soni , R. 1966 . Formulas and Theorems for the Special Functions of Mathematical Physics Springer‐Verlag .
  • 2004 . Maple . MapleSoft. Version 9.51
  • Mika , J. 1961 . Neutron transport with anistropic scattering . Nucl. Sci. Eng. , 11 : 415 – 427 .
  • Press , W. , Teukolsky , S. , Vetterling , W. and Flannery , B. 1996 . Numerical Recipes in C , 2nd edn. Cambridge University Press .
  • Siewert , C. 1980 . On computing eigenvalues in radiative transfer . J. Math. Phys. , 21 ( 9 ) : 2468 – 2470 .
  • Toh , K.‐C. and Trefethen , L. 1994 . Pseudozeros of polynomials and pseudospectra of companion matrices . Numerische Mathematik , 68 : 403 – 425 .
  • Van den Eynde , G. 2005 . Neutron Transport with Anisotropic Scattering PhD thesis, Université Libre de Bruxelles .

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