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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 10, Pages 1643–1655 (Mi zvmmf11140)  

General numerical methods

Choice of finite-difference schemes in solving coefficient inverse problems

A. F. Albu, Yu. G. Evtushenko, V. I. Zubov

Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, 119333 Russia

Abstract: Various choices of a finite-difference scheme for approximating the heat diffusion equation in solving a three-dimensional coefficient inverse problem were studied. A comparative analysis was conducted for several alternating direction schemes, such as locally one-dimensional, Douglas–Rachford, and Peaceman–Rachford schemes, as applied to nonlinear problems for the three-dimensional heat equation with temperature-dependent coefficients. Each numerical method was used to compute the temperature distribution inside a parallelepiped. The methods were compared in terms of the accuracy of the resulting solution and the computation time required for achieving the prescribed accuracy on a computer.

Key words: nonlinear problems, three-dimensional heat equation, numerical methods, alternating direction schemes.

DOI: https://doi.org/10.31857/S004446692010004X


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:10, 1589–1600

Bibliographic databases:

UDC: 533.6.011.5
Received: 31.01.2020
Revised: 21.03.2020
Accepted:09.06.2020

Citation: A. F. Albu, Yu. G. Evtushenko, V. I. Zubov, “Choice of finite-difference schemes in solving coefficient inverse problems”, Zh. Vychisl. Mat. Mat. Fiz., 60:10 (2020), 1643–1655; Comput. Math. Math. Phys., 60:10 (2020), 1589–1600

Citation in format AMSBIB
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