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.
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Albu, A.F., Evtushenko, Y.G. & Zubov, V.I. Choice of Finite-Difference Schemes in Solving Coefficient Inverse Problems. Comput. Math. and Math. Phys. 60, 1589–1600 (2020). https://doi.org/10.1134/S0965542520100048
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DOI: https://doi.org/10.1134/S0965542520100048