Analytical solutions for the neutron transport using the spectral methods
type: Item
instance of: scholarly article
title: Analytical solutions for the neutron transport using the spectral methods
zbMATH Open document ID: 1114.35043
DOI: 10.1155/IJMMS/2006/16214
author: Abdelouahab Kadem
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2007-06-14T00:00:00Z
full work available at URL: https://eudml.org/doc/53151
review text: Summary: We present a method for solving the two-dimensional equation of transfer. The method can be extended easily to the general linear transport problem. The used technique allows us to reduce the two-dimensional equation to a system of one-dimensional equations. The idea of using the spectral method for searching for solutions to the multidimensional transport problems leads us to a solution for all values of the independent variables, the proposed method reduces the solution of the multidimensional problems into a set of one-dimensional ones that have well-established deterministic solutions. The procedure is based on the development of the angular flux in truncated series of Chebyshev polynomials which will permit us to transform the two-dimensional problem into a set of one-dimensional problems.
Mathematics Subject Classification ID: 35F15
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 5164258
zbMATH Keywords: spectral method
zbMATH Keywords: truncated series
zbMATH Keywords: Chebyshev polynomials
MaRDI profile type: Publication
cites work: Q5508799
cites work: Chebyshev spectral-\(S_N\) method for the neutron transport equation
cites work: Spectral approximation for elliptic boundary value problems
cites work: Chebyshev and Fourier spectral methods.
cites work: Q4039908
cites work: Q3242006
cites work: Q4888881
cites work: Q4199478
cites work: Q3446193
cites work: Q3542188
cites work: Solution of the three‐dimensional transport equation using the spectral methods
cites work: Elementary Solutions of the Reduced Three-Dimensional Transport Equation
cites work: A Chebyshev spectral method for radiative transfer equations applied to electromagnetic wave propagation and scattering in a discrete random medium
cites work: Chebyshev spectral methods for radiative transfer
cites work: Q3725507
description: scientific article; zbMATH DE number 5164258