Open Access
ARTICLE
Determination of Time-Dependent Coefficients for a Weakly Degenerate Heat Equation
M. J. Huntul1, D. Lesnic2, *
1 Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia.
2 Department of Applied Mathematics, University of Leeds, Leeds, LS2 9JT, UK.
* Corresponding Author: D. Lesnic. Email: .
Computer Modeling in Engineering & Sciences 2020, 123(2), 475-494. https://doi.org/10.32604/cmes.2020.08791
Received 10 October 2019; Accepted 17 March 2020; Issue published 01 May 2020
Abstract
In this paper, we consider solving numerically for the first time inverse problems
of determining the time-dependent thermal diffusivity coefficient for a weakly degenerate
heat equation, which vanishes at the initial moment of time, and/or the convection
coefficient along with the temperature for a one-dimensional parabolic equation, from
some additional information about the process (the so-called over-determination
conditions). Although uniquely solvable these inverse problems are still ill-posed since
small changes in the input data can result in enormous changes in the output solution.
The finite difference method with the Crank-Nicolson scheme combined with the
nonlinear Tikhonov regularization are employed. The resulting minimization problem is
computationally solved using the MATLAB toolbox routine
lsqnonlin. For both exact
and noisy input data, accurate and stable numerical results are obtained.
Keywords
Cite This Article
Huntul, M. J., Lesnic, D. (2020). Determination of Time-Dependent Coefficients for a Weakly Degenerate Heat Equation.
CMES-Computer Modeling in Engineering & Sciences, 123(2), 475–494. https://doi.org/10.32604/cmes.2020.08791