Simultaneous determination of time-dependent coefficients in the heat equation
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Publication Date
Fri Oct 14 2016
Journal Name
International Journal For Computational Methods In Engineering Science And Mechanics
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Publication Date
Fri Apr 01 2016
Journal Name
Communications In Nonlinear Science And Numerical Simulation
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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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Publication Date
Mon May 01 2017
Journal Name
Applied Mathematics And Computation
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Publication Date
Tue Mar 16 2021
Journal Name
International Journal For Computational Methods In Engineering Science And Mechanics
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Publication Date
Mon Jan 01 2024
Journal Name
2nd International Conference For Engineering Sciences And Information Technology (esit 2022): Esit2022 Conference Proceedings
Publication Date
Thu Nov 30 2023
Journal Name
Iraqi Journal Of Science
Determination of Spacewise− Dependent Heat Source Term in Pseudoparabolic Equation from Overdetermination Conditions
Pseudo-parabolic equation
Inverse problem
von Neumann stability analysis
Finite difference method
Tikhonov regularization method
This paper examines the finding of spacewise dependent heat source function in pseudoparabolic equation with initial and homogeneous Dirichlet boundary conditions, as well as the final time value / integral specification as additional conditions that ensure the uniqueness solvability of the inverse problem. However, the problem remains ill-posed because tiny perturbations in input data cause huge errors in outputs. Thus, we employ Tikhonov’s regularization method to restore this instability. In order to choose the best regularization parameter, we employ L-curve method. On the other hand, the direct (forward) problem is solved by a finite difference scheme while the inverse one is reformulated as an optimization problem. The
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Publication Date
Tue Apr 01 2014
Journal Name
International Communications In Heat And Mass Transfer
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Publication Date
Thu Jul 01 2021
Journal Name
Iraqi Journal Of Science
Simultaneous Identification of Thermal Conductivity and Heat Source in the Heat Equation
Inverse problem
Heat equation
Heat flux
Tikhonov regularization
Nonlinear optimization
This paper presents a numerical solution to the inverse problem consisting of recovering time-dependent thermal conductivity and heat source coefficients in the one-dimensional parabolic heat equation. This mathematical formulation ensures that the inverse problem has a unique solution. However, the problem is still ill-posed since small errors in the input data lead to a drastic amount of errors in the output coefficients. The finite difference method with the Crank-Nicolson scheme is adopted as a direct solver of the problem in a fixed domain. The inverse problem is solved sub
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