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Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method

Author

Listed:
  • Benedict Barnes
  • Isaac Addai
  • Francis Ohene Boateng
  • Ishmael Takyi
  • Ram Jiwari

Abstract

The Quasi-Reversibility Regularization Method (Q-RRM) provides stable approximate solution of the Cauchy problem of the Helmholtz equation in the Hilbert space by providing either additional information in the Laplace-type operator in the Helmholtz equation or the imposed Cauchy boundary conditions on the Helmholtz equation. To help bridge this gap in the literature, a Modified Quasi-reversibility Regularization Method (MQ-RRM) is introduced to provide additional information in both the Laplace-type operator occurring in the Helmholtz equation and the imposed Cauchy boundary conditions on the Helmholtz equation, resulting in a strong stable solution and faster convergence of the solution of the Helmholtz equation than the regularized solutions provided by Q-RRM and its variants methods.

Suggested Citation

  • Benedict Barnes & Isaac Addai & Francis Ohene Boateng & Ishmael Takyi & Ram Jiwari, 2022. "Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method," Journal of Mathematics, Hindawi, vol. 2022, pages 1-15, December.
    • Handle: RePEc:hin:jjmath:5336305
    DOI: 10.1155/2022/5336305
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