Development of a Gauss-Chandrasekhar Quadrature for the Boundary Sources Method with Anisotropic Scattering

References

• Brezinski , C. 1978 . Algorithmes d'accélération de la convergence, étude numérique , Paris : Editions technip .
   Google Scholar
• Case , K. and Zweifel , P. 1967 . Linear transport theory , Reading, MA : Addison-Wesley .
   Google Scholar
• Davis , P. and Rabinowitz , Ph. 1984 . Methods of numerical integration, , 2nd ed , Academic Press .
   Google Scholar
• De Doncker , E. and Piessens , R. 1976 . Algorithm 32: Automatic computation of integrals with singular integrand over a finite or an infinite range . Computing , 17 : 265 – 279 .
   Google Scholar
• Golub , J. and Welsch , J. 1969 . Calculation of Gauss quadrature rules . Math. Comput , 23 : 221 – 230 .
   Web of Science ®Google Scholar
• Henyey , L. and Greenstein , J. 1941 . Diffuse radiation in the galaxy . Astrophysics Journal , 93 : 70 – 83 .
   Web of Science ®Google Scholar
• Inönü , E. 1970 . Orthogonality of a set of polynomials encountered in neutron-transport and radiative-transfer theories . Journal of Mathematical Physics , 11 ( 2 ) : 568 – 577 .
   Web of Science ®Google Scholar
• Iri , M. , Moriguti , S. and Takasawa , Y. 1987 . On a certain quadrature formula . Journal of Computational and Applied Mathematics , 17 : 3 – 20 .
   Web of Science ®Google Scholar
• Laurie , D. 1996 . Anti-Gaussian quadrature formulas . Mathematics of Computation , 65 ( 214 ) : 739 – 747 .
   Google Scholar
• Mika , J. 1961 . Neutron transport with anistropic scattering . Nuclear Science and Engineering , 11 : 415 – 427 .
   Web of Science ®Google Scholar
• Montagnini , B. 2005 . Nuclear reactor physics, a collection of papers dedicated to Silvio Edoardo Corno: , 11 – 114 . Torino : GLUT .
   Google Scholar
• Murota , K. and Iri , M. 1982 . Parameter tuning and repeated application of the IMT-type transformation in numerical quadrature . Numerische Mathematik , 38 : 347 – 363 .
   Google Scholar
• Ooura , T. and Mori , M. 1991 . The double exponential formula for oscillatory functions over the half infinite interval . Journal of Computational and Applied Mathematics , 38 : 353 – 360 .
   Web of Science ®Google Scholar
• Piessens , R. , Doncker de Kapenga , E. , Uberhuber , C. and Kahaner , D. 1983 . Quadpack, a subroutine package for automatic integration , Springer-Verlag .
   Google Scholar
• Seward , J. and Nethercote , N. 2004 . Valgrind, version 2.2.0 http://valgrind.org(accessed on June 2005)
   Google Scholar
• Takahasi , H. and Mori , M. 1974 . Double exponential formulas for numerical integration . Publ RIMS Kyoto University , 9 : 721 – 741 .
   Google Scholar
• Van , d en , Eynde , G. , Beauwens , R. and Mund , E. 2007 . The boundary source method with anisotropic scattering . Nuclear Science and Engineering , 155 : 300 – 309 .
   Google Scholar
• Van , d en , Eynde , G. , Beauwens , R. and Mund , E. H. 2007 . Calculating the discrete spectrum of the transport operator with arbitrary-order anisotropic scattering . Transport Theory and Statistical Physics , 36 : 1 – 19 .
   Google Scholar
• Wynn , P. 1966 . On the convergence and stability of the epsilon algorithm . J. SIAM Numerical Analysis , 3 ( 1 ) : 91 – 122 .
   Google Scholar