Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method
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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/5336305 |
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| Summary: | 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. |
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| ISSN: | 2314-4785 |