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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2019 Volume 59, Number 5, Page 859 (Mi zvmmf10897)

This article is cited in 6 papers

Inverse problem of finding the coecient of the lowest term in two-dimensional heat equation with Ionkin-type boundary condition

M. I. Ismailova, S. Erkovanb

a Gebze Technical University, Department of Mathematics, 41400, Gebze/Kocaeli, Turkey
b Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, AZ1141 Baku, Azerbaijan

Abstract: We consider an inverse problem of determining the time-dependent lowest order coefficient of two-dimensional (2D) heat equation with Ionkin boundary and total energy integral overdetermination condition. The global well-posedness of the problem is obtained by generalized Fourier method combined with the unique solvability of the second kind Volterra integral equation. For obtaining a numerical solution of the inverse problem, we propose the discretization method from a new combination. On the one hand, it is known the traditional method of uniform finite difference combined with numerical integration on a uniform grid (trapezoidal and Simpson's), on the other hand, we give the method of non-uniform finite difference is combined by a numerical integration on a non-uniform grid (with Gauss–Lobatto nodes). Numerical examples illustrate how to implement the method.

Key words: 2D heat equation, Volterra integral equation, Ionkin-type boundary condition, generalized Fourier method, uniform finite difference method, non-uniform finite difference method, numerical integration.

Received: 13.02.2017
Revised: 25.06.2018
Accepted: 11.01.2019

Language: English

DOI: 10.1134/S0044466919050168


 English version:
Computational Mathematics and Mathematical Physics, 2019, 59:5, 791–808

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