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Fourier Truncation Regularization Method for a Three-Dimensional Cauchy Problem of the Modified Helmholtz Equation with Perturbed Wave Number

Author

Listed:
  • Fan Yang

    (School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China)

  • Ping Fan

    (School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China)

  • Xiao-Xiao Li

    (School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, China)

Abstract

In this paper, the Cauchy problem of the modified Helmholtz equation (CPMHE) with perturbed wave number is considered. In the sense of Hadamard, this problem is severely ill-posed. The Fourier truncation regularization method is used to solve this Cauchy problem. Meanwhile, the corresponding error estimate between the exact solution and the regularized solution is obtained. A numerical example is presented to illustrate the validity and effectiveness of our methods.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:705-:d:255123
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    References listed on IDEAS

    as
    1. Xiao-Xiao Li & Fan Yang & Jie Liu & Lan Wang, 2013. "The Quasireversibility Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, April.
    2. 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.
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