Note on the Solution of Transport Equation by Tau Method and Walsh Functions

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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Main Authors: Abdelouahab Kadem, Adem Kilicman
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2010/704168
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spelling doaj-0edd77c2a8b94a059dc19839adf681612020-11-24T22:16:59ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author Abdelouahab Kadem
Adem Kilicman
spellingShingle Abdelouahab Kadem
Adem Kilicman
Note on the Solution of Transport Equation by Tau Method and Walsh Functions
Abstract and Applied Analysis
author_facet Abdelouahab Kadem
Adem Kilicman
author_sort Abdelouahab Kadem
title 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_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_sort note on the solution of transport equation by tau method and walsh functions
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2010-01-01
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.
url http://dx.doi.org/10.1155/2010/704168
work_keys_str_mv AT abdelouahabkadem noteonthesolutionoftransportequationbytaumethodandwalshfunctions
AT ademkilicman noteonthesolutionoftransportequationbytaumethodandwalshfunctions
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