Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-697711120210301The time-dependent diffusion equation: An inverse diffusivity problem33543949810.22067/ijnao.2021.11309.0ENS.H. TabasiSchool of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364,
Damghan, Iran.H.D. MazraehSchool of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364,
Damghan, Iran.0000-0001-9619-4134A.A. IraniSchool of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364,
Damghan, Iran.R. PourgholiSchool of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364,
Damghan, Iran.0000-0003-4111-5130A. EsfahaniSchool of Mathematics and Computer Science, Damghan University, P.O.Box 36715-364,
Damghan, Iran.Journal Article20200205We find a solution of an unknown time-dependent diffusivity <em>a</em>(<em>t</em>) 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 <em>a</em>(<em>t</em>) in (<em>a</em>(<em>t</em>)<em>, T </em>(<em>x, t</em>)), which is a solution to the corresponding problem. Then, an optimal estimation for unknown <em>a</em>(<em>t</em>) 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.https://ijnao.um.ac.ir/article_39498_4e70303762f92c47958ef68e7d4ce560.pdf