On the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes
In this article, we have presented a variable step finite difference method for solving second order boundary value problems in ordinary differential equations. We have discussed the convergence and established that proposed has at least cubic order of accuracy. The proposed method tested on severa...
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| Format: | Article |
| Language: | English |
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Qubahan
2021-03-01
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| Series: | Qubahan Academic Journal |
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| Online Access: | https://journal.qubahan.com/index.php/qaj/article/view/19 |
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| _version_ | 1832544454513262592 |
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| author | Pramod Pandey |
| author_facet | Pramod Pandey |
| author_sort | Pramod Pandey |
| collection | DOAJ |
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In this article, we have presented a variable step finite difference method for solving second order boundary value problems in ordinary differential equations. We have discussed the convergence and established that proposed has at least cubic order of accuracy. The proposed method tested on several model problems for the numerical solution. The numerical results obtained for these model problems with known / constructed exact solution confirm the theoretical conclusions of the proposed method. The computational results obtained for these model problems suggest that method is efficient and accurate.
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| format | Article |
| id | doaj-art-04f5822fb6f54bf4a452998b1c7a9a54 |
| institution | Kabale University |
| issn | 2709-8206 |
| language | English |
| publishDate | 2021-03-01 |
| publisher | Qubahan |
| record_format | Article |
| series | Qubahan Academic Journal |
| spelling | doaj-art-04f5822fb6f54bf4a452998b1c7a9a542025-02-03T10:12:57ZengQubahanQubahan Academic Journal2709-82062021-03-011110.48161/qaj.v1n1a1919On the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodesPramod Pandey0Dyal Singh College (Univ. of Delhi) In this article, we have presented a variable step finite difference method for solving second order boundary value problems in ordinary differential equations. We have discussed the convergence and established that proposed has at least cubic order of accuracy. The proposed method tested on several model problems for the numerical solution. The numerical results obtained for these model problems with known / constructed exact solution confirm the theoretical conclusions of the proposed method. The computational results obtained for these model problems suggest that method is efficient and accurate. https://journal.qubahan.com/index.php/qaj/article/view/19Boundary Value Problem, Convergence of the Method, Cubic Order, Finite Difference Method, Nonuniform Step Length. |
| spellingShingle | Pramod Pandey On the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes Qubahan Academic Journal Boundary Value Problem, Convergence of the Method, Cubic Order, Finite Difference Method, Nonuniform Step Length. |
| title | On the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes |
| title_full | On the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes |
| title_fullStr | On the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes |
| title_full_unstemmed | On the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes |
| title_short | On the numerical solution of two point boundary value problem for the Helmholtz type equation by finite difference method with non regular step length between nodes |
| title_sort | on the numerical solution of two point boundary value problem for the helmholtz type equation by finite difference method with non regular step length between nodes |
| topic | Boundary Value Problem, Convergence of the Method, Cubic Order, Finite Difference Method, Nonuniform Step Length. |
| url | https://journal.qubahan.com/index.php/qaj/article/view/19 |
| work_keys_str_mv | AT pramodpandey onthenumericalsolutionoftwopointboundaryvalueproblemforthehelmholtztypeequationbyfinitedifferencemethodwithnonregularsteplengthbetweennodes |