The time-dependent diffusion equation: An inverse diffusivity problem

Iranian Journal of Numerical Analysis and Optimization

مقاله 2، دوره 11، شماره 1 - شماره پیاپی 19، خرداد 2021، صفحه 33-54   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.11309.0

نویسندگان

S.H. Tabasi^* ؛ H.D. Mazraeh؛ A.A. Irani؛ R. Pourgholi؛ A. Esfahani

School of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364, Damghan, Iran.

چکیده

We find a solution of an unknown time-dependent diffusivity a(t) in a linear inverse parabolic problem by a modified genetic algorithm. At first, it is shown that under certain conditions of data, there exists at least one solution for unknown a(t) in (a(t), T (x, t)), which is a solution to the corresponding problem. Then, an optimal estimation for unknown a(t) is found by applying the least-squares method and a modified genetic algo rithm. Results show that an excellent estimation can be obtained by the implementation of a modified real-valued genetic algorithm within an Intel Pentium (R) dual-core CPU with a clock speed of 2.4 GHz.

کلیدواژه‌ها

Inverse parabolic problem؛ Existence؛ Uniqueness؛ Green’s function؛ Fixed point؛ Contraction mapping؛ Genetic algorithm

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