Reconstruction of time-dependent coefficients from heat moments
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(15)
Publication Date
Fri Oct 14 2016
Journal Name
International Journal For Computational Methods In Engineering Science And Mechanics
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Publication Date
Sat Mar 01 2014
Journal Name
Computers & Mathematics With Applications
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(29)
Publication Date
Tue Mar 16 2021
Journal Name
International Journal For Computational Methods In Engineering Science And Mechanics
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Publication Date
Thu Jun 01 2023
Journal Name
Partial Differential Equations In Applied Mathematics
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Publication Date
Thu Jan 01 2015
Journal Name
Finite Difference Methods,theory And Applications
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(1)
Publication Date
Fri Apr 01 2016
Journal Name
Communications In Nonlinear Science And Numerical Simulation
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(10)
Publication Date
Tue Apr 01 2014
Journal Name
International Communications In Heat And Mass Transfer
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(10)
Publication Date
Tue Mar 30 2021
Journal Name
Iraqi Journal Of Science
Numerical Solution to Recover Time-dependent Coefficient and Free Boundary from Nonlocal and Stefan Type Overdetermination Conditions in Heat Equation
inverse problem
coefficient identification problem
nonlinear optimization
FDM
This paper investigates the recovery for time-dependent coefficient and free boundary for heat equation. They are considered under mass/energy specification and Stefan conditions. The main issue with this problem is that the solution is unstable and sensitive to small contamination of noise in the input data. The Crank-Nicolson finite difference method (FDM) is utilized to solve the direct problem, whilst the inverse problem is viewed as a nonlinear optimization problem. The latter problem is solved numerically using the routine optimization toolbox lsqnonlin from MATLAB. Consequently, the Tikhonov regularization method is used in order to gain stable solutions. The results were compared with their exact solution and tested via
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(10)
(2)
Publication Date
Tue May 30 2023
Journal Name
Iraqi Journal Of Science
Reconstruction of Timewise Dependent Coefficient and Free Boundary in Nonlocal Diffusion Equation with Stefan and Heat Flux as Overdetermination Conditions
Inverse problem
Free boundary
Nonlocal diffusion equation
Stefan condition
Implicit finite difference scheme
Tikhonov technique
Stability analysis
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 app
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(2)
Publication Date
Wed Jan 01 2020
Journal Name
International Journal Of Mathematical Modelling And Numerical Optimisation
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