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Landweber iterative method for identifying the initial value problem of the time-space fractional diffusion-wave equation

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Abstract

This paper considers the inverse problem for identifying the initial value problem of a space-time fractional diffusion wave equation. In general, this problem is ill-posed and the Landweber iterative regularization method is used to solve this problem. The error estimates between the exact solution and the regularized solution are given under the a priori parameter choice rule and the a posteriori parameter choice rule, respectively. In order to verify the validity and stability of the used method, numerical examples of two different dimensional cases with experimental data are performed.

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Authors and Affiliations

  1. School of Science, Lanzhou University of Technology, Lanzhou, Gansu, 730050, People’s Republic of China

    Fan Yang, Yan Zhang & Xiao-Xiao Li

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  1. Fan Yang
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  2. Yan Zhang
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  3. Xiao-Xiao Li
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Correspondence to Fan Yang.

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Yang, F., Zhang, Y. & Li, XX. Landweber iterative method for identifying the initial value problem of the time-space fractional diffusion-wave equation. Numer Algor 83, 1509–1530 (2020). https://doi.org/10.1007/s11075-019-00734-6

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  • DOI: https://doi.org/10.1007/s11075-019-00734-6

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