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Simultaneous determination for a space-dependent heat source and the initial data by the MFS |
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| Affiliation: | 1. Department of Applied Mathematics, National Research Centre, Dokki, Cairo 12622, Egypt;2. Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg 620002, Russia;3. Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt;1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;2. Department of Mathematics and Statistics, Auburn University, Auburn, USA;1. School of Science, Hunan University of Technology, Zhuzhou, 412007, Hunan, PR China;2. School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, PR China |
| Abstract: | In this paper we propose a numerical algorithm based on the method of fundamental solutions for recovering a space-dependent heat source and the initial data simultaneously in an inverse heat conduction problem. The problem is transformed into a homogeneous backward-type inverse heat conduction problem and a Dirichlet boundary value problem for Poisson's equation. We use an improved method of fundamental solutions to solve the backward-type inverse heat conduction problem and apply the finite element method for solving the well-posed direct problem. The Tikhonov regularization method combined with the generalized cross validation rule for selecting a suitable regularization parameter is applied to obtain a stable regularized solution for the backward-type inverse heat conduction problem. Numerical experiments for four examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed algorithm. |
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