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The Quasireversibility Regularization Method for Identifying the Unknown Source for the Modified Helmholtz Equation

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  • Xiao-Xiao Li
  • Fan Yang
  • Jie Liu
  • Lan Wang

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 quasireversibility 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

  • 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.
    • Handle: RePEc:hin:jnljam:245963
    DOI: 10.1155/2013/245963
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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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