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The Simplified Tikhonov Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation

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  • Fan Yang
  • HengZhen Guo
  • XiaoXiao Li

Abstract

This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the simplified Tikhonov regularization method. Convergence estimate is presented between the exact solution and the regularization solution. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.

Suggested Citation

  • Fan Yang & HengZhen Guo & XiaoXiao Li, 2011. "The Simplified Tikhonov Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-14, June.
    • Handle: RePEc:hin:jnlmpe:953492
    DOI: 10.1155/2011/953492
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    Cited by:

    1. Fan Yang & Ping Fan & Xiao-Xiao Li, 2019. "Fourier Truncation Regularization Method for a Three-Dimensional Cauchy Problem of the Modified Helmholtz Equation with Perturbed Wave Number," Mathematics, MDPI, vol. 7(8), pages 1-8, August.

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