M. J. Huntul1, D. Lesnic2, *
CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.2, pp. 475-494, 2020, DOI:10.32604/cmes.2020.08791
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… More >
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