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Abstract
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Article Information:
Determination of an Unknown Radiation Term in a Nonlinear Inverse Problem using Simulation of Markov Chains
Morteza Ebrahimi
Corresponding Author: Morteza Ebrahimi
Submitted: December 02, 2011
Accepted: December 23, 2011
Published: May 01, 2012 |
Abstract:
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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
Taylor’s 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.
Key words: Finite difference scheme, Markov chain, Monte Carlo method, nonlinear inverse problem, radiation term, ,
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Abstract
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Cite this Reference:
Morteza Ebrahimi, . Determination of an Unknown Radiation Term in a Nonlinear Inverse Problem using Simulation of Markov Chains. Research Journal of Applied Sciences, Engineering and Technology, (09): 1131-1136.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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