Analytical solutions for the neutron transport using the spectral methods
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...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/16214 |
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| _version_ | 1832559199060492288 |
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| author | Abdelouahab Kadem |
| author_facet | Abdelouahab Kadem |
| author_sort | Abdelouahab Kadem |
| collection | DOAJ |
| description | 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 independant 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. |
| format | Article |
| id | doaj-art-38259b58e4e542dea47c3fda7d1fd8f0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-38259b58e4e542dea47c3fda7d1fd8f02025-02-03T01:30:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/1621416214Analytical solutions for the neutron transport using the spectral methodsAbdelouahab Kadem0Department of Mathematics, Faculty of Sciences, University of Sétif, Sétif 19000, AlgeriaWe 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 independant 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.http://dx.doi.org/10.1155/IJMMS/2006/16214 |
| spellingShingle | Abdelouahab Kadem Analytical solutions for the neutron transport using the spectral methods International Journal of Mathematics and Mathematical Sciences |
| title | Analytical solutions for the neutron transport using the spectral methods |
| title_full | Analytical solutions for the neutron transport using the spectral methods |
| title_fullStr | Analytical solutions for the neutron transport using the spectral methods |
| title_full_unstemmed | Analytical solutions for the neutron transport using the spectral methods |
| title_short | Analytical solutions for the neutron transport using the spectral methods |
| title_sort | analytical solutions for the neutron transport using the spectral methods |
| url | http://dx.doi.org/10.1155/IJMMS/2006/16214 |
| work_keys_str_mv | AT abdelouahabkadem analyticalsolutionsfortheneutrontransportusingthespectralmethods |