An efficient and accurate modified Adomian decomposition method for solving the Helmholtz equation with high-wavenumber
This paper presents a modified Adomian decomposition method (MADM) for solving the one and two-dimensional Helmholtz equation with large wavenumbers. The standard Adomian decomposition method (ADM) suffers from severe divergence issues as the wavenumber increases, which limits its applicability for...
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2024-04-01
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| Series: | Surveys in Mathematics and its Applications |
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| Online Access: | https://www.utgjiu.ro/math/sma/v19/p19_08.pdf |
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| author | Saleem Nasser Alomari Yahya Qaid Hasan |
| author_facet | Saleem Nasser Alomari Yahya Qaid Hasan |
| author_sort | Saleem Nasser Alomari |
| collection | DOAJ |
| description | This paper presents a modified Adomian decomposition method (MADM) for solving the one and two-dimensional Helmholtz equation with large wavenumbers. The standard Adomian decomposition method (ADM) suffers from severe divergence issues as the wavenumber increases, which limits its applicability for high-frequency problems. MADM overcomes this drawback by introducing a novel modification technique that enhances the convergence and accuracy of the solution. Several numerical examples are provided to demonstrate the effectiveness and superiority of MADM over ADM for solving the Helmholtz equation with various boundary conditions and wavenumbers. |
| format | Article |
| id | doaj-art-c5fa1bae986d495db600e6f8084df0c8 |
| institution | DOAJ |
| issn | 1843-7265 1842-6298 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | University Constantin Brancusi of Targu-Jiu |
| record_format | Article |
| series | Surveys in Mathematics and its Applications |
| spelling | doaj-art-c5fa1bae986d495db600e6f8084df0c82025-08-20T02:50:30ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982024-04-0119 (2024)143161An efficient and accurate modified Adomian decomposition method for solving the Helmholtz equation with high-wavenumberSaleem Nasser Alomari 0 Yahya Qaid Hasan1Department of Mathematics, Faculty of Education and Sciences, Albaydha University, Albaydha, Yemen.Department of Mathematics, Faculty of Applied Sciences, Thamar University, Thamar, YemenThis paper presents a modified Adomian decomposition method (MADM) for solving the one and two-dimensional Helmholtz equation with large wavenumbers. The standard Adomian decomposition method (ADM) suffers from severe divergence issues as the wavenumber increases, which limits its applicability for high-frequency problems. MADM overcomes this drawback by introducing a novel modification technique that enhances the convergence and accuracy of the solution. Several numerical examples are provided to demonstrate the effectiveness and superiority of MADM over ADM for solving the Helmholtz equation with various boundary conditions and wavenumbers. https://www.utgjiu.ro/math/sma/v19/p19_08.pdfhelmholtz equationmodified adomian decomposition methodlarge wavenumbers |
| spellingShingle | Saleem Nasser Alomari Yahya Qaid Hasan An efficient and accurate modified Adomian decomposition method for solving the Helmholtz equation with high-wavenumber Surveys in Mathematics and its Applications helmholtz equation modified adomian decomposition method large wavenumbers |
| title | An efficient and accurate modified Adomian decomposition method for solving the Helmholtz equation with high-wavenumber |
| title_full | An efficient and accurate modified Adomian decomposition method for solving the Helmholtz equation with high-wavenumber |
| title_fullStr | An efficient and accurate modified Adomian decomposition method for solving the Helmholtz equation with high-wavenumber |
| title_full_unstemmed | An efficient and accurate modified Adomian decomposition method for solving the Helmholtz equation with high-wavenumber |
| title_short | An efficient and accurate modified Adomian decomposition method for solving the Helmholtz equation with high-wavenumber |
| title_sort | efficient and accurate modified adomian decomposition method for solving the helmholtz equation with high wavenumber |
| topic | helmholtz equation modified adomian decomposition method large wavenumbers |
| url | https://www.utgjiu.ro/math/sma/v19/p19_08.pdf |
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