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- Title
Reconstruction of Timewise Dependent Coefficient and Free Boundary in Nonlocal Diffusion Equation with Stefan and Heat Flux as Overdetermination Conditions.
- Authors
Qahtan, Jehan A.; Hussein, M. S.
- Abstract
The problem of reconstruction of a timewise dependent coefficient and free boundary at once in a nonlocal diffusion equation under Stefan and heat Flux as nonlocal overdetermination conditions have been considered. A Crank–Nicolson finite difference method (FDM) combined with the trapezoidal rule quadrature is used for the direct problem. While the inverse problem is reformulated as a nonlinear regularized least-square optimization problem with simple bound and solved efficiently by MATLAB subroutine lsqnonlin from the optimization toolbox. Since the problem under investigation is generally ill-posed, a small error in the input data leads to a huge error in the output, then Tikhonov’s regularization technique is applied to obtain regularized stable results.
- Subjects
HEAT flux; FINITE difference method; INVERSE problems; QUADRATURE domains; TRANSPORT equation; TIKHONOV regularization; FINITE differences; HEAT equation
- Publication
Iraqi Journal of Science, 2023, Vol 64, Issue 5, p2449
- ISSN
0067-2904
- Publication type
Article
- DOI
10.24996/ijs.2023.64.5.30