Optimal error bound and generalized Tikhonov regularization for identifying an unknown source in the heat equation

Journal of Mathematical Chemistry ◽

10.1007/s10910-010-9774-3 ◽

2010 ◽

Vol 49 (3) ◽

pp. 765-775 ◽

Author(s):

Ailin Qian ◽

Yan Li

Keyword(s):

Heat Equation ◽

Error Bound ◽

Tikhonov Regularization ◽

Optimal Error ◽

Unknown Source ◽

Optimal Error Bound

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Optimal error bound and Fourier regularization for identifying an unknown source in the heat equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2009.01.008 ◽

2009 ◽

Vol 230 (2) ◽

pp. 728-737 ◽

Author(s):

Fang-Fang Dou ◽

Chu-Li Fu ◽

Feng-Lian Yang

Keyword(s):

Heat Equation ◽

Error Bound ◽

Optimal Error ◽

Unknown Source ◽

Optimal Error Bound

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Optimal error bound and simplified Tikhonov regularization method for a backward problem for the time-fractional diffusion equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2014.11.026 ◽

2015 ◽

Vol 279 ◽

pp. 277-292 ◽

Author(s):

Jun-Gang Wang ◽

Ting Wei ◽

Yu-Bin Zhou

Keyword(s):

Diffusion Equation ◽

Error Bound ◽

Tikhonov Regularization ◽

Regularization Method ◽

Fractional Diffusion ◽

Tikhonov Regularization Method ◽

Optimal Error ◽

Backward Problem ◽

Time Fractional Diffusion Equation ◽

Optimal Error Bound

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Stationary iterated weighted Tikhonov regularization method for identifying an unknown source term of time-fractional radial heat equation

Numerical Algorithms ◽

10.1007/s11075-021-01213-7 ◽

2021 ◽

Author(s):

Shuping Yang ◽

Xiangtuan Xiong ◽

Ping Pan ◽

Yue Sun

Keyword(s):

Heat Equation ◽

Tikhonov Regularization ◽

Regularization Method ◽

Source Term ◽

Tikhonov Regularization Method ◽

Unknown Source ◽

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Optimal Error Bound and A Semi-discrete Difference Scheme for the Cauchy Problem of the Modified Helmholtz Equation

Proceedings of the 2017 International Conference on Manufacturing Engineering and Intelligent Materials (ICMEIM 2017) ◽

10.2991/icmeim-17.2017.32 ◽

2017 ◽

Author(s):

Ai-lin Qian ◽

Zi-min Chen

Keyword(s):

Cauchy Problem ◽

Difference Scheme ◽

Helmholtz Equation ◽

Error Bound ◽

Optimal Error ◽

Modified Helmholtz Equation ◽

The Cauchy Problem ◽

Optimal Error Bound

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Determination of an Unknown Source in the Heat Equation by the Method of Tikhonov Regularization in Hilbert Scales

Journal of Applied Mathematics and Physics ◽

10.4236/jamp.2014.22002 ◽

2014 ◽

Vol 02 (02) ◽

pp. 10-17

Author(s):

Zhenyu Zhao ◽

Ou Xie ◽

Zehong Meng ◽

Lei You

Keyword(s):

Heat Equation ◽

Tikhonov Regularization ◽

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A potential-free field inverse time-fractional Schrödinger problem: optimal error bound analysis and regularization method

Authorea ◽

10.22541/au.158801044.47478041 ◽

2020 ◽

Author(s):

Fan Yang ◽

Junliang Fu ◽

Xiao Xiao Li

Keyword(s):

Error Bound ◽

Regularization Method ◽

Optimal Error ◽

Error Bound Analysis ◽

Optimal Error Bound ◽

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An optimal error bound for a finite element approximation of spatially extended predator-prey interaction model

Numerical Algorithms ◽

10.1007/s11075-019-00810-x ◽

2019 ◽

Vol 85 (1) ◽

pp. 209-229

Author(s):

Ahmed A. Al Ghafli ◽

Hassan J. Al Salman

Keyword(s):

Finite Element ◽

Error Bound ◽

Interaction Model ◽

Finite Element Approximation ◽

Element Approximation ◽

Optimal Error ◽

Predator Prey ◽

Spatially Extended ◽

Prey Interaction ◽

Optimal Error Bound

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On Tikhonov’s method and optimal error bound for inverse source problem for a time-fractional diffusion equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2020.02.024 ◽

2020 ◽

Vol 80 (1) ◽

pp. 61-81

Author(s):

Nguyen Minh Dien ◽

Dinh Nguyen Duy Hai ◽

Tran Quoc Viet ◽

Dang Duc Trong

Keyword(s):

Diffusion Equation ◽

Error Bound ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Inverse Source Problem ◽

Optimal Error ◽

Time Fractional Diffusion Equation ◽

Optimal Error Bound

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A potential-free field inverse Schrödinger problem: optimal error bound analysis and regularization method

Inverse Problems in Science and Engineering ◽

10.1080/17415977.2019.1700243 ◽

2019 ◽

Vol 28 (9) ◽

pp. 1209-1252 ◽

Author(s):

Fan Yang ◽

Jun-Liang Fu ◽

Xiao-Xiao Li

Keyword(s):

Error Bound ◽

Regularization Method ◽

Optimal Error ◽

Error Bound Analysis ◽

Optimal Error Bound ◽

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OPTIMAL ERROR BOUND AND APPROXIMATION METHODS FOR A CAUCHY PROBLEM OF THE MODIFIED HELMHOLTZ EQUATION

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691311004080 ◽

2011 ◽

Vol 09 (02) ◽

pp. 305-315 ◽

Author(s):

AILIN QIAN ◽

YUJIANG WU

Keyword(s):

Cauchy Problem ◽

Helmholtz Equation ◽

Error Estimates ◽

Error Bound ◽

Optimality Theory ◽

Tikhonov Regularization Method ◽

Regularization Methods ◽

Optimal Error ◽

Modified Helmholtz Equation ◽

Optimal Error Bound

We consider a Cauchy problem for a modified Helmholtz equation, especially when we give the optimal error bound for this problem. Some spectral regularization methods and a revised Tikhonov regularization method are used to stabilize the problem from the viewpoint of general regularization theory. Hölder-type stability error estimates are provided for these regularization methods. According to the optimality theory of regularization, the error estimates are order optimal.

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