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A Regularization Method to Solve a Cauchy Problem for the Two-Dimensional Modified Helmholtz Equation

Author

Listed:
  • Shangqin He

    (School of Mathematics and Statistics, NingXia University, Yinchuan 750021, China
    College of Mathematics and Information Science and Technology, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China)

  • Xiufang Feng

    (School of Mathematics and Statistics, NingXia University, Yinchuan 750021, China)

Abstract

In this paper, the ill-posed problem of the two-dimensional modified Helmholtz equation is investigated in a strip domain. For obtaining a stable numerical approximation solution, a mollification regularization method with the de la Vallée Poussin kernel is proposed. An error estimate between the exact solution and approximation solution is given under suitable choices of the regularization parameter. Two numerical experiments show that our procedure is effective and stable with respect to perturbations in the data.

Suggested Citation

  • Shangqin He & Xiufang Feng, 2019. "A Regularization Method to Solve a Cauchy Problem for the Two-Dimensional Modified Helmholtz Equation," Mathematics, MDPI, vol. 7(4), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:360-:d:224636
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