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 Simultaneous identification of diffusion coefficient, spacewise dependent source and initial value for one-dimensional heat equation Zhao, Zhi-Xue1,2; Banda, Mapundi K.2; Guo, Bao-Zhu3,4 2017-07-15 Source Publication MATHEMATICAL METHODS IN THE APPLIED SCIENCES ISSN 0170-4214 Volume 40Issue:10Pages:3552-3565 Abstract This paper deals with an inverse problem of determining the diffusion coefficient, spacewise dependent source term, and the initial value simultaneously for a one-dimensional heat equation based on the boundary control, boundary measurement, and temperature distribution at a given single instant in time. By a Dirichlet series representation for the boundary observation, the identification of the diffusion coefficient and initial value can be transformed into a spectral estimation problem of an exponential series with measurement error, which is solved by the matrix pencil method. For the identification of the source term, a finite difference approximation method in conjunction with the truncated singular value decomposition is adopted, where the regularization parameter is determined by the generalized cross-validation criterion. Numerical simulations are performed to verify the result of the proposed algorithm. Copyright (c) 2016 John Wiley & Sons, Ltd. Keyword Inverse Problem Matrix Pencil Method Finite Difference Method Truncated Singular Value Decomposition Generalized Cross-validation DOI 10.1002/mma.4245 Language 英语 Funding Project National Natural Science Foundation of China ; Doctoral Fund Program of Tianjin Normal University[52XB1413] ; National Research Foundation of South Africa ; National Research Foundation of South Africa ; University of Pretoria WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000402801800011 Publisher WILEY Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/25711 Collection 系统科学研究所 Affiliation 1.Tianjin Normal Univ, Sch Math Sci, Tianjin 300387, Peoples R China2.Univ Pretoria, Dept Math & Appl Math, ZA-0002 Pretoria, South Africa3.Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China4.Univ Witwatersrand, Sch Comp Sci & Appl Math, Johannesburg, South Africa Recommended CitationGB/T 7714 Zhao, Zhi-Xue,Banda, Mapundi K.,Guo, Bao-Zhu. Simultaneous identification of diffusion coefficient, spacewise dependent source and initial value for one-dimensional heat equation[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2017,40(10):3552-3565. APA Zhao, Zhi-Xue,Banda, Mapundi K.,&Guo, Bao-Zhu.(2017).Simultaneous identification of diffusion coefficient, spacewise dependent source and initial value for one-dimensional heat equation.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,40(10),3552-3565. MLA Zhao, Zhi-Xue,et al."Simultaneous identification of diffusion coefficient, spacewise dependent source and initial value for one-dimensional heat equation".MATHEMATICAL METHODS IN THE APPLIED SCIENCES 40.10(2017):3552-3565.