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Inverse problem of finding the coefficient 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
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.
2D heat equation, Volterra integral equation, Ionkin-type boundary condition, generalized Fourier method, uniform finite difference method, non-uniform finite difference method, numerical integration.
Computational Mathematics and Mathematical Physics, 2019, 59:5, 791–808
M. I. Ismailov, S. Erkovan, “Inverse problem of finding the coefficient of the lowest term in two-dimensional heat equation with Ionkin-type boundary condition”, Zh. Vychisl. Mat. Mat. Fiz., 59:5 (2019), 859; Comput. Math. Math. Phys., 59:5 (2019), 791–808
Citation in format AMSBIB
\by M.~I.~Ismailov, S.~Erkovan
\paper Inverse problem of finding the coefficient of the lowest term in two-dimensional heat equation with Ionkin-type boundary condition
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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