Solving a time-fractional inverse heat conduction problem with an unknown nonlinear boundary condition
Publish place: Journal of Mathematical Modeling، Vol: 7، Issue: 1
Publish Year: 1398
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JMMO-7-1_006
تاریخ نمایه سازی: 19 خرداد 1403
Abstract:
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.
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Authors
Afshin Babaei
Faculty of MAthematical sciences, University of Mazandaran, Babolsar, Iran.