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.
Babaei, A. (2019). Solving a time-fractional inverse heat conduction problem with an unknown nonlinear boundary condition. Journal of Mathematical Modeling, 7(1), 85-106. doi: 10.22124/jmm.2018.11656.1204
MLA
Afshin Babaei. "Solving a time-fractional inverse heat conduction problem with an unknown nonlinear boundary condition". Journal of Mathematical Modeling, 7, 1, 2019, 85-106. doi: 10.22124/jmm.2018.11656.1204
HARVARD
Babaei, A. (2019). 'Solving a time-fractional inverse heat conduction problem with an unknown nonlinear boundary condition', Journal of Mathematical Modeling, 7(1), pp. 85-106. doi: 10.22124/jmm.2018.11656.1204
VANCOUVER
Babaei, A. Solving a time-fractional inverse heat conduction problem with an unknown nonlinear boundary condition. Journal of Mathematical Modeling, 2019; 7(1): 85-106. doi: 10.22124/jmm.2018.11656.1204
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