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Quasi-reversibility and truncation methods to solve a Cauchy problem for the modified Helmholtz equation

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  • Qin, Hai-Hua
  • Wei, Ting

Abstract

In this paper, the Cauchy problem for the modified Helmholtz equation in a rectangular domain is investigated. We use a quasi-reversibility method and a truncation method to solve it and present convergence estimates under two different a priori boundedness assumptions for the exact solution. The numerical results show that our proposed numerical methods work effectively.

Suggested Citation

  • Qin, Hai-Hua & Wei, Ting, 2009. "Quasi-reversibility and truncation methods to solve a Cauchy problem for the modified Helmholtz equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 352-366.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:2:p:352-366
    DOI: 10.1016/j.matcom.2009.07.005
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    Cited by:

    1. Hongwu Zhang & Xiaoju Zhang, 2019. "Generalized Tikhonov Method and Convergence Estimate for the Cauchy Problem of Modified Helmholtz Equation with Nonhomogeneous Dirichlet and Neumann Datum," Mathematics, MDPI, vol. 7(8), pages 1-19, July.

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