Solving a time-fractional inverse heat conduction problem with an unknown nonlinear boundary condition

	Solving a time-fractional inverse heat conduction problem with an unknown nonlinear boundary condition
Journal of Mathematical Modeling
مقاله 15، دوره 7، شماره 1، خرداد 2019، صفحه 85-106 اصل مقاله (1.13 M)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2018.11656.1204
نویسنده
Afshin Babaei^*
Faculty of MAthematical sciences, University of Mazandaran, Babolsar, Iran.
چکیده
In this paper, we consider a time-fractional inverse heat conduction problem with an unknown function in the nonlinear boundary condition. First, ill-posedness of this problem is shown. Thus, we will apply the mollification regularization method with Gauss kernel to regularize the problem, then the space marching finite difference method is considered to solve numerically the mollified problem. The generalized cross-validation choice rule is used to find a suitable regularization parameter. The numerical scheme is completely described and the stability and convergence of the solutions are investigated. Finally, some numerical examples are presented to illustrate the validity and effectiveness of the proposed algorithm.
کلیدواژه‌ها
Inverse problem؛ Caputo's fractional derivative؛ Ill-posedness؛ Mollification؛ convergence Analysis

آمار تعداد مشاهده مقاله: 766 تعداد دریافت فایل اصل مقاله: 853

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