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Original Articles

An Iterative Algorithm for the Backward Heat Conduction Problem Based on Variable Relaxation Factors

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Pages 293-308 | Published online: 18 Oct 2010

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Jin Wen, Masahiro Yamamoto & Ting Wei. (2013) Simultaneous determination of a time-dependent heat source and the initial temperature in an inverse heat conduction problem. Inverse Problems in Science and Engineering 21:3, pages 485-499.
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Jianhua Zhou, Yuwen Zhang, J.K. Chen & Z.C. Feng. (2012) Inverse Estimation of Surface Temperature Induced by a Moving Heat Source in a 3-D Object Based on Back Surface Temperature with Random Measurement Errors. Numerical Heat Transfer, Part A: Applications 61:2, pages 85-100.
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Jin Wen. (2011) A meshless method for reconstructing the heat source and partial initial temperature in heat conduction. Inverse Problems in Science and Engineering 19:7, pages 1007-1022.
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Chih‐Wen Chang, Chein‐Shan Liu & Jiang‐Ren Chang. (2010) A quasi‐boundary semi‐analytical method for backward heat conduction problems. Journal of the Chinese Institute of Engineers 33:2, pages 163-175.
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Articles from other publishers (29)

Walter C. Simo Tao Lee. (2023) A variational technique of mollification applied to backward heat conduction problems. Applied Mathematics and Computation 449, pages 127917.
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Mohammed Hamaidi, Ahmed Naji, Fatima Ghafrani & Mostafa Jourhmane. (2020) Noniterative Localized and Space-Time Localized RBF Meshless Method to Solve the Ill-Posed and Inverse Problem. Modelling and Simulation in Engineering 2020, pages 1-11.
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Fan Yang, Ya-Ru Sun, Xiao-Xiao Li & Can-Yun Huang. (2018) The quasi-boundary value method for identifying the initial value of heat equation on a columnar symmetric domain. Numerical Algorithms 82:2, pages 623-639.
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Yung-Wei Chen. (2019) A backward-forward Lie-group shooting method for nonhomogeneous multi-dimensional backward heat conduction problems under a long time span. International Journal of Heat and Mass Transfer 133, pages 226-246.
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Yung-Wei Chen. (2018) A modified Lie-group shooting method for multi-dimensional backward heat conduction problems under long time span. International Journal of Heat and Mass Transfer 127, pages 948-960.
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Yung-Wei Chen. (2018) A highly accurate backward-forward algorithm for multi-dimensional backward heat conduction problems in fictitious time domains. International Journal of Heat and Mass Transfer 120, pages 499-514.
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Xiangtuan Xiong, Jinmei Li & Jin Wen. (2017) Some novel linear regularization methods for a deblurring problem. Inverse Problems and Imaging 11:2, pages 403-426.
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Yung-Wei Chen. (2016) High order implicit and explicit Lie-group schemes for solving backward heat conduction problems. International Journal of Heat and Mass Transfer 101, pages 1016-1029.
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Nguyen Huy Tuan, Bui Thanh Duy, Nguyen Dang Minh & Vo Anh Khoa. (2015) Hölder stability for a class of initial inverse nonlinear heat problem in multiple dimension. Communications in Nonlinear Science and Numerical Simulation 23:1-3, pages 89-114.
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Chein-Shan Liu & Chih-Wen Chang. (2015) Nonlinear problems with unknown initial temperature and without final temperature, solved by the GL ( N , ) shooting method . International Journal of Heat and Mass Transfer 83, pages 665-678.
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Guang-Hui Zheng & Ting Wei. (2014) Recovering the source and initial value simultaneously in a parabolic equation. Inverse Problems 30:6, pages 065013.
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Davood Rostamy & Kobra Karimi. (2014) A new operational matrix method based on the Bernstein polynomials for solving the backward inverse heat conduction problems. International Journal of Numerical Methods for Heat & Fluid Flow 24:3, pages 669-678.
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H. W. Zhang & T. Wei. (2013) Two iterative methods for a Cauchy problem of the elliptic equation with variable coefficients in a strip region. Numerical Algorithms 65:4, pages 875-892.
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Zohar Zafrir & Sharon Zlochiver. (2013) Reconstruction of retrospective cardiac activity-numerical study in a single cell and in a linear strand. International Journal for Numerical Methods in Biomedical Engineering 29:6, pages 683-697.
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Tuan Nguyen Huy, Quan Pham Hoang, Trong Dang Duc & Triet Le Minh. (2013) On a backward heat problem with time-dependent coefficient: Regularization and error estimates. Applied Mathematics and Computation 219:11, pages 6066-6073.
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Ming Li & Xiangtuan Xiong. (2012) On a fractional backward heat conduction problem: Application to deblurring. Computers & Mathematics with Applications 64:8, pages 2594-2602.
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Hai-Hua Qin & Ting Wei. (2011) Some filter regularization methods for a backward heat conduction problem. Applied Mathematics and Computation 217:24, pages 10317-10327.
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B.T. Johansson, D. Lesnic & T. Reeve. (2011) A comparative study on applying the method of fundamental solutions to the backward heat conduction problem. Mathematical and Computer Modelling 54:1-2, pages 403-416.
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Ailin Qian & Jianfeng Mao. (2011) Quasi-Reversibility Regularization Method for Solving a Backward Heat Conduction Problem. American Journal of Computational Mathematics 01:03, pages 159-162.
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Chih-Wen Chang & Chein-Shan Liu. (2010) A new algorithm for direct and backward problems of heat conduction equation. International Journal of Heat and Mass Transfer 53:23-24, pages 5552-5569.
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Ming Li, Tongsong Jiang & Y.C. Hon. (2010) A meshless method based on RBFs method for nonhomogeneous backward heat conduction problem. Engineering Analysis with Boundary Elements 34:9, pages 785-792.
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Xiao-Li Feng, Zhi Qian & Chu-Li Fu. (2008) Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded region. Mathematics and Computers in Simulation 79:2, pages 177-188.
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M. Tadi. (2008) An iterative method for the solution of ill-posed parabolic systems. Applied Mathematics and Computation 201:1-2, pages 843-851.
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Chu-Li Fu, Xiang-Tuan Xiong & Zhi Qian. (2007) Fourier regularization for a backward heat equation. Journal of Mathematical Analysis and Applications 331:1, pages 472-480.
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Jiang-Ren Chang, Chein-Shan Liu & Chih-Wen Chang. (2007) A new shooting method for quasi-boundary regularization of backward heat conduction problems. International Journal of Heat and Mass Transfer 50:11-12, pages 2325-2332.
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XIANG-TUAN XIONG & CHU-LI FU. (2011) ERROR ESTIMATES ON A BACKWARD HEAT EQUATION BY A WAVELET DUAL LEAST SQUARES METHOD. International Journal of Wavelets, Multiresolution and Information Processing 05:03, pages 389-397.
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Xiang-Tuan Xiong, Chu-Li Fu & Zhi Qian. (2006) Two numerical methods for solving a backward heat conduction problem. Applied Mathematics and Computation 179:1, pages 370-377.
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Xiang-Tuan Xiong, Chu-Li Fu, Zhi Qian & Xiang Gao. (2006) Error estimates of a difference approximation method for a backward heat conduction problem. International Journal of Mathematics and Mathematical Sciences 2006, pages 1-9.
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