1403/03/25
سمیه نعمتی

سمیه نعمتی

مرتبه علمی: دانشیار
ارکید:
تحصیلات: دکترای تخصصی
اسکاپوس:
دانشکده: دانشکده علوم ریاضی
نشانی:
تلفن: 01135302419

مشخصات پژوهش

عنوان
A numerical Algorithm Based on Chebyshev Polynomials for Solving some Inverse Source Problems
نوع پژوهش
JournalPaper
کلیدواژه‌ها
Parabolic equation‎ , Inverse problem‎ , ‎ Unknown source term‎ , ‎ Tikhonov regularization‎ , Chebyshev polynomials‎ , ‎ Operational matrix.
سال
2016
مجله پژوهش های ریاضی
شناسه DOI
پژوهشگران Somayeh Nemati ، Afshin Babaei ، Salameh Sedaghat

چکیده

‎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