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Two iterative methods for a Cauchy problem of the elliptic equation with variable coefficients in a strip region

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Abstract

We investigate a Cauchy problem for the elliptic equation with variable coefficients. This problem is severely ill-posed in the sense of Hadamard and the regularization techniques are required to stabilize numerical computations. We give two iterative methods to deal with it. Under an a-priori and an a-posteriori selection rule for the regularization parameter, the convergence rates of two algorithms are obtained. Numerical results show that two methods work well.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou city, Gansu Province, 730000, People’s Republic of China

    H. W. Zhang & T. Wei

  2. School of Mathematics and Statistics, Hexi University, Zhangye city, Gansu Province, 734000, People’s Republic of China

    H. W. Zhang

Authors
  1. H. W. Zhang
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  2. T. Wei
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Correspondence to T. Wei.

Additional information

The work described in this paper was supported by the NSF of China (10971089, 11171136) and the YTSRF of Hexi university (QN2011-10).

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Zhang, H.W., Wei, T. Two iterative methods for a Cauchy problem of the elliptic equation with variable coefficients in a strip region. Numer Algor 65, 875–892 (2014). https://doi.org/10.1007/s11075-013-9719-6

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  • DOI: https://doi.org/10.1007/s11075-013-9719-6

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