Volume 2, Issue 1 (9-2016)                   mmr 2016, 2(1): 47-68 | Back to browse issues page


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Nemati S, Babaei A, Sedaghat S. A numerical Algorithm Based on Chebyshev Polynomials for Solving some Inverse Source Problems. mmr 2016; 2 (1) :47-68
URL: http://mmr.khu.ac.ir/article-1-2577-en.html
Abstract:   (4184 Views)

In this paper‎, two inverse problems of determining an unknown source term in a parabolic‎ equation are considered‎. ‎First‎, ‎the unknown source term is ‎estimated in the form of a combination of Chebyshev functions‎. ‎Then‎, ‎a numerical algorithm based on Chebyshev polynomials is presented for obtaining the solution of the problem‎. ‎For solving the problem‎, ‎the operational matrices of integration and derivation are introduced and utilized to reduce the mentioned problem into the matrix equations which correspond to a system of linear algebraic equations with unknown Chebyshev coefficients‎. Due‎ to ill-posedness of these inverse problems‎, ‎the Tikhonov regularization method with generalized cross validation (GCV) criterion is applied to find stable‎ solutions. ‎Finally‎, some examples are presented to illustrate the efficiency of this numerical method‎. The numerical results show that the proposed method is a reliable method and can give high accuracy approximate solutions.

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Type of Study: S | Subject: alg
Received: 2017/01/16 | Revised: 2017/09/13 | Accepted: 2017/01/16 | Published: 2017/01/16 | ePublished: 2017/01/16

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