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 |
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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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| _version_ | 1850179261071097856 |
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| author | Benedict Barnes Isaac Addai Francis Ohene Boateng Ishmael Takyi |
| author_facet | Benedict Barnes Isaac Addai Francis Ohene Boateng Ishmael Takyi |
| author_sort | Benedict Barnes |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9f3cd8477c074f6889d6533a6c3c6a13 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9f3cd8477c074f6889d6533a6c3c6a132025-08-20T02:18:33ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5336305Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization MethodBenedict Barnes0Isaac Addai1Francis Ohene Boateng2Ishmael Takyi3Mathematics DepartmentMathematics DepartmentDepartment of Mathematics EducationMathematics DepartmentThe 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.http://dx.doi.org/10.1155/2022/5336305 |
| spellingShingle | Benedict Barnes Isaac Addai Francis Ohene Boateng Ishmael Takyi Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method Journal of Mathematics |
| title | Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method |
| title_full | Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method |
| title_fullStr | Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method |
| title_full_unstemmed | Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method |
| title_short | Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method |
| title_sort | solving the helmholtz equation together with the cauchy boundary conditions by a modified quasi reversibility regularization method |
| url | http://dx.doi.org/10.1155/2022/5336305 |
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