Note on the Solution of Transport Equation by Tau Method and Walsh Functions
We consider the combined Walsh function for the three-dimensional case. A method for the solution of the neutron transport equation in three-dimensional case by using the Walsh function, Chebyshev polynomials, and the Legendre polynomials are considered. We also present Tau method, and it was proved...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/704168 |
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| _version_ | 1832548032701267968 |
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| author | Abdelouahab Kadem Adem Kilicman |
| author_facet | Abdelouahab Kadem Adem Kilicman |
| author_sort | Abdelouahab Kadem |
| collection | DOAJ |
| description | We consider the combined Walsh function for the three-dimensional case. A method for the solution of the neutron transport equation in three-dimensional case by using the Walsh function, Chebyshev polynomials, and the Legendre polynomials are considered. We also present Tau method, and it was proved that it is a good approximate to exact solutions. This method is based on expansion of the angular flux in a truncated series of Walsh function in the angular variable. The main characteristic of this technique is that it reduces the problems to those of solving a system of algebraic equations; thus, it is greatly simplifying the problem. |
| format | Article |
| id | doaj-art-0edd77c2a8b94a059dc19839adf68161 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0edd77c2a8b94a059dc19839adf681612025-02-03T06:42:20ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/704168704168Note on the Solution of Transport Equation by Tau Method and Walsh FunctionsAbdelouahab Kadem0Adem Kilicman1L.M.F.N Mathematics Department, University of Setif, Setif 19000, AlgeriaDepartment of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), Serdang, Selangor 43400, MalaysiaWe consider the combined Walsh function for the three-dimensional case. A method for the solution of the neutron transport equation in three-dimensional case by using the Walsh function, Chebyshev polynomials, and the Legendre polynomials are considered. We also present Tau method, and it was proved that it is a good approximate to exact solutions. This method is based on expansion of the angular flux in a truncated series of Walsh function in the angular variable. The main characteristic of this technique is that it reduces the problems to those of solving a system of algebraic equations; thus, it is greatly simplifying the problem.http://dx.doi.org/10.1155/2010/704168 |
| spellingShingle | Abdelouahab Kadem Adem Kilicman Note on the Solution of Transport Equation by Tau Method and Walsh Functions Abstract and Applied Analysis |
| title | Note on the Solution of Transport Equation by Tau Method and Walsh Functions |
| title_full | Note on the Solution of Transport Equation by Tau Method and Walsh Functions |
| title_fullStr | Note on the Solution of Transport Equation by Tau Method and Walsh Functions |
| title_full_unstemmed | Note on the Solution of Transport Equation by Tau Method and Walsh Functions |
| title_short | Note on the Solution of Transport Equation by Tau Method and Walsh Functions |
| title_sort | note on the solution of transport equation by tau method and walsh functions |
| url | http://dx.doi.org/10.1155/2010/704168 |
| work_keys_str_mv | AT abdelouahabkadem noteonthesolutionoftransportequationbytaumethodandwalshfunctions AT ademkilicman noteonthesolutionoftransportequationbytaumethodandwalshfunctions |