Notes on a new approximate solution of 2-D heat equation backward in time |
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| Authors: | Nguyen Huy Tuan Dang Duc Trong Pham Hoang Quan |
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| Institution: | 1. Institute for Computational Science and Technology, Quarter 6, Linh Trung Ward, Thu Duc District, HoChiMinh City, Viet Nam;2. Department of Mathematics, University of Natural Science, Vietnam National University, 227 Nguyen Van Cu, Q.5, HoChiMinh City, Viet Nam;3. Department of Mathematics and Applications, Sai Gon University, 273 An Duong Vuong, Q.5, HoChiMinh City, Viet Nam;4. Department of Mathematics, Hochiminh University of Technology, 144/24 Dien Bien Phu, P.25, Binh Thanh Dist., HoChiMinh City, Viet Nam |
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| Abstract: | In this paper, we consider a backward heat problem that appears in many applications. This problem is ill-posed. The solution of the problem as the solution exhibits unstable dependence on the given data functions. Using a new regularization method, we regularize the problem and get some new error estimates. Some numerical tests illustrate that the proposed method is feasible and effective. This work is a generalization of many recent papers, including the earlier paper A new regularized method for two dimensional nonhomogeneous backward heat problem, Appl. Math. Comput. 215(3) (2009) 873–880] and some other authors such as Chu-Li Fu et al. , and , Campbell et al. 4]. |
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| Keywords: | Backward heat problem Nonhomogeneous heat equation Ill-posed problem Quasi-boundary value method Quasi-reversibility method Error estimate |
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