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Original Articles

An optimal method for fractional heat conduction problem backward in time

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Pages 823-840 | Received 14 Mar 2011, Accepted 25 Jun 2011, Published online: 21 Jul 2011

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Read on this site (6)

Jin Wen, Xue-Juan Ren & Shi-Juan Wang. (2022) Simultaneous determination of source term and initial value in the heat conduction problem by modified quasi-reversibility regularization method. Numerical Heat Transfer, Part B: Fundamentals 82:3-4, pages 112-127.
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Zhousheng Ruan & Zewen Wang. (2017) Identification of a time-dependent source term for a time fractional diffusion problem. Applicable Analysis 96:10, pages 1638-1655.
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Fan Yang, Chu-Li Fu & Xiao-Xiao Li. (2015) The inverse source problem for time-fractional diffusion equation: stability analysis and regularization. Inverse Problems in Science and Engineering 23:6, pages 969-996.
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Ming Yang & Jijun Liu. (2015) Fourier regularization for a final value time-fractional diffusion problem. Applicable Analysis 94:7, pages 1508-1526.
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Xiangtuan Xiong, Xiaoyan Fan & Ming Li. (2015) Spectral method for ill-posed problems based on the balancing principle. Inverse Problems in Science and Engineering 23:2, pages 292-306.
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Articles from other publishers (18)

Xiaoli Feng, Xiaoyu Yuan, Meixia Zhao & Zhi Qian. (2024) Numerical methods for the forward and backward problems of a time-space fractional diffusion equation. Calcolo 61:1.
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Yu Qiao & Xiangtuan Xiong. (2023) Simultaneous determination of the space-dependent source and initial value for a two-dimensional heat conduction equation. Computers & Mathematics with Applications 147, pages 25-37.
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Jin Wen, Chong-Wang Yue, Zhuan-Xia Liu & Shi-Juan Wang. (2023) FRACTIONAL TIKHONOV REGULARIZATION METHOD FOR SIMULTANEOUS INVERSION OF THE SOURCE TERM AND INITIAL DATA IN A TIME-FRACTIONAL DIFFUSION EQUATION. Rocky Mountain Journal of Mathematics 53:1.
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Jin Wen, Xue-Juan Ren & Shi-Juan Wang. (2023) Simultaneous determination of source term and the initial value in the space-fractional diffusion problem by a novel modified quasi-reversibility regularization method. Physica Scripta 98:2, pages 025201.
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Jin Wen, Zhuan-Xia Liu, Chong-Wang Yue & Shi-Juan Wang. (2021) Landweber iteration method for simultaneous inversion of the source term and initial data in a time-fractional diffusion equation. Journal of Applied Mathematics and Computing 68:5, pages 3219-3250.
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佳琪 侯. (2021) Two Regularization Methods for the Two-Dimensional Time-Inverse Heat Conduction Problem and Its Posterior Error Estimation. Pure Mathematics 11:12, pages 1974-1986.
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Fan Yang, Pan Zhang, Xiao-Xiao Li & Xin-Yi Ma. (2020) Tikhonov regularization method for identifying the space-dependent source for time-fractional diffusion equation on a columnar symmetric domain. Advances in Difference Equations 2020:1.
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Hongwu Zhang & Xiaoju Zhang. (2020) Solving the Riesz–Feller space-fractional backward diffusion problem by a generalized Tikhonov method. Advances in Difference Equations 2020:1.
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G Floridia & M Yamamoto. (2020) Backward problems in time for fractional diffusion-wave equation. Inverse Problems 36:12, pages 125016.
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Nguyen Minh Dien, Dinh Nguyen Duy Hai, Tran Quoc Viet & Dang Duc Trong. (2020) On Tikhonov’s method and optimal error bound for inverse source problem for a time-fractional diffusion equation. Computers & Mathematics with Applications 80:1, pages 61-81.
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Fan Yang, Ni Wang, Xiao-Xiao Li & Can-Yun Huang. (2019) A quasi-boundary regularization method for identifying the initial value of time-fractional diffusion equation on spherically symmetric domain. Journal of Inverse and Ill-posed Problems 27:5, pages 609-621.
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Xiangtuan Xiong, Xuemin Xue & Zhi Qian. (2017) A modified iterative regularization method for ill-posed problems. Applied Numerical Mathematics 122, pages 108-128.
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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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Zhousheng Ruan, Zhijian Yang & Xiliang Lu. (2015) An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation. Advances in Applied Mathematics and Mechanics 8:1, pages 1-18.
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Zhousheng Ruan, Jerry Zhijian Yang & Xiliang Lu. (2015) Tikhonov Regularisation Method for Simultaneous Inversion of the Source Term and Initial Data in a Time-Fractional Diffusion Equation. East Asian Journal on Applied Mathematics 5:3, pages 273-300.
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Zhousheng Ruan, Zewen Wang & Wen Zhang. (2015) A Directly Numerical Algorithm for a Backward Time-Fractional Diffusion Equation Based on the Finite Element Method. Mathematical Problems in Engineering 2015, pages 1-8.
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Xiangtuan Xiong, Liping Zhao & Y.C. Hon. (2014) Stability estimate and the modified regularization method for a Cauchy problem of the fractional diffusion equation. Journal of Computational and Applied Mathematics 272, pages 180-194.
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Ming Yang & Jijun Liu. (2013) Solving a final value fractional diffusion problem by boundary condition regularization. Applied Numerical Mathematics 66, pages 45-58.
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