A numerical Algorithm Based on Chebyshev Polynomials for Solving some Inverse Source Problems
| Autor: | S Nemati, A Babaei, S Sedaghat |
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| Jazyk: | perština |
| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | پژوهشهای ریاضی, Vol 2, Iss 1, Pp 47-68 (2016) |
| Druh dokumentu: | article |
| ISSN: | 2588-2546 2588-2554 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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