Approximate Solutions of Transport Problems. II. Convergence and Applications of the Discrete Ordinate Method

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Previous article Next article Approximate Solutions of Transport Problems. II. Convergence and Applications of the Discrete Ordinate MethodHerbert B. KellerHerbert B. Kellerhttps://doi.org/10.1137/0108005PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] N. I. Achieser, Theory of approximation, Translated by Charles J. Hyman, Frederick Ungar Publishing Co., New York, 1956x+307 MR0095369 0072.28403 Google Scholar[2] K. M. Case, , F. de Hoffmann and , G. Placzek, Introduction to the theory of neutron diffusion. Vol. I, Los Alamos Scientific Laboratory, Los Alamos, N. M., 1953viii+174 MR0070494 Google Scholar[3] S. Chandrasekhar, Radiative Transfer, Oxford University Press, 1950xiv+393, London MR0042603 0037.43201 Google Scholar[4] B. Davison and , J. B. Sykes, Neutron transport theory, Oxford, at the Clarendon Press, 1957xx+450, London MR0095716 0077.22505 Google Scholar[5] R. A. Frazier, , W. J. Duncan and , A. R. Collar, Elementary Matrices, Cambridge Univ. Press, London, 1957 Google Scholar[6] R. Gast, On the equivalence of the spherical harmonics method and the discrete ordinate method using Gauss quadrature for the Boltzmann equation, WAPD-TM-118, Westinghouse Electric Corp. Bettis Plant, 1958 Google Scholar[7] F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill, New York, 1956 0070.12401 Google Scholar[8] E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944viii+558 MR0010757 0063.02971 Google Scholar[9] Herbert B. Keller, Approximate solutions of transport problems. I. Steady-state, elastic scattering in plane and spherical geometry, J. Soc. Indust. Appl. Math., 6 (1958), 452–465 10.1137/0106029 MR0106547 LinkISIGoogle Scholar[10] W. Kofink, Studies of the spherical harmonics method in neutron transport theory., Nuovo Cimento (10), 9 (1958), 497–541 MR0104375 CrossrefGoogle Scholar[11] V. Kourganoff, Basic methods in transfer problems. Radiative equilibrium and neutron diffusion, Oxford, at the Clarendon Press, 1952xv+281 MR0054158 0048.20105 Google Scholar[12] Robert D. Richtmyer, Difference methods for initial-value problems, Interscience tracts in pure and applied mathematics. Iract 4, Interscience Publishers, Inc., New. York, 1957xii+238 MR0093918 0079.33702 Google Scholar[13] S. Schechter, On the inversion of certain matrices, NYO-2539, AEC Computing and Applied Mathematics Center, Institute of Mathematical Sciences, New York Univ., 1959 Google Scholar[14] D. Schiff and , S. Stein, Escape probability and capture fraction for grey slabs, WAPD-149, Westinghouse Electric Corporation, Bettis Plant, 1956 Google Scholar[15] G. C. Wick, Über ebene Diffusions-probleme, Z. Phys., 121 (1943), 702–718 10.1007/BF01339167 MR0010052 0028.36602 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: Discrete-Ordinate MethodSIAM Journal on Numerical Analysis, Vol. 36, No. 5 | 25 July 2006AbstractPDF (507 KB)Convergence of Inner Iterations for Finite-Difference Approximations to the Linear Transport EquationSIAM Journal on Numerical Analysis, Vol. 23, No. 5 | 14 July 2006AbstractPDF (568 KB)Error Estimates for the Combined Spatial and Angular Approximations of the Transport Equation for Slab GeometrySIAM Journal on Numerical Analysis, Vol. 20, No. 5 | 17 July 2006AbstractPDF (2411 KB)Convergence Properties of Discrete-Ordinates Solutions for Neutron Transport in Three-Dimensional MediaSIAM Journal on Numerical Analysis, Vol. 17, No. 1 | 17 July 2006AbstractPDF (1302 KB)Theoretical Properties of One-Dimensional Discrete OrdinatesSIAM Journal on Numerical Analysis, Vol. 16, No. 2 | 31 July 2006AbstractPDF (1642 KB)Convergence of the Discrete-Ordinates Method for Anisotropically Scattering Multiplying Particles in a Subcritical SlabSIAM Journal on Numerical Analysis, Vol. 10, No. 1 | 14 July 2006AbstractPDF (590 KB)Pointwise Convergence of the Three-Dimensional Discrete Ordinate MethodSIAM Journal on Numerical Analysis, Vol. 8, No. 2 | 14 July 2006AbstractPDF (360 KB)On the Pointwise Convergence of the Discrete-Ordinate MethodHerbert B. KellerJournal of the Society for Industrial and Applied Mathematics, Vol. 8, No. 4 | 10 July 2006AbstractPDF (545 KB)On the Convergence of the Discrete Ordinate MethodBurton WendroffJournal of the Society for Industrial and Applied Mathematics, Vol. 8, No. 3 | 10 July 2006AbstractPDF (304 KB) Volume 8, Issue 1| 1960Journal of the Society for Industrial and Applied Mathematics1-223 History Submitted:30 April 1959Published online:10 July 2006 InformationCopyright © 1960 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0108005Article page range:pp. 43-73ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics