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2012 (Vol. 4, Issue: 09)
Article Information:

Determination of an Unknown Radiation Term in a Nonlinear Inverse Problem using Simulation of Markov Chains

Morteza Ebrahimi
Corresponding Author:  Morteza Ebrahimi 

Key words:  Finite difference scheme, Markov chain, Monte Carlo method, nonlinear inverse problem, radiation term, ,
Vol. 4 , (09): 1131-1136
Submitted Accepted Published
December 02, 2011 December 23, 2011 May 01, 2012
Abstract:

The purpose of the present study is to provide a fast and accurate algorithm for identifying the medium temperature and the unknown radiation term from an overspecified condition on the boundary in an inverse problem of linear heat equation with nonlinear boundary condition. The design of the paper is to employ Taylorís series expansion for linearize nonlinear term and then finite-difference approximation to discretize the problem domain. Owing to the application of the finite difference scheme, a large sparse system of linear algebraic equations is obtained. An approach of Monte Carlo method is employed to solve the linear system and estimate unknown radiation term. The Monte Carlo optimization is adopted to modify the estimated values. Results show that a good estimation on the radiation term can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.
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  Cite this Reference:
Morteza Ebrahimi, 2012. Determination of an Unknown Radiation Term in a Nonlinear Inverse Problem using Simulation of Markov Chains.  Research Journal of Applied Sciences, Engineering and Technology, 4(09): 1131-1136.
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ISSN (Online):  2040-7467
ISSN (Print):   2040-7459
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