Adomian decomposition method for solving initial value problems in vibration models
A number of engineering problems have second-order ordinary differential equations as their mathematical models. In practice, we may have a large scale problem with a large number of degrees of freedom, which must be solved accurately. Therefore, treating the mathematical model governing the problem...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2018-01-01
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| Series: | MATEC Web of Conferences |
| Online Access: | https://doi.org/10.1051/matecconf/201815902007 |
| _version_ | 1818886139825618944 |
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| author | Mungkasi Sudi Ekaputra I Made Wicaksana |
| author_facet | Mungkasi Sudi Ekaputra I Made Wicaksana |
| author_sort | Mungkasi Sudi |
| collection | DOAJ |
| description | A number of engineering problems have second-order ordinary differential equations as their mathematical models. In practice, we may have a large scale problem with a large number of degrees of freedom, which must be solved accurately. Therefore, treating the mathematical model governing the problems correctly is required in order to get an accurate solution. In this work, we use Adomian decomposition method to solve vibration models in the forms of initial value problems of second-order ordinary differential equations. However, for problems involving an external source, the Adomian decomposition method may not lead to an accurate solution if the external source is not correctly treated. In this paper, we propose a strategy to treat the external source when we implement the Adomian decomposition method to solve initial value problems of second-order ordinary differential equations. Computational results show that our strategy is indeed effective. We obtain accurate solutions to the considered problems. Note that exact solutions are often not available, so they need to be approximated using some methods, such as the Adomian decomposition method. |
| first_indexed | 2024-12-19T16:16:35Z |
| format | Article |
| id | doaj.art-6a0f0d21efa14a83b9d396baaf61ae6b |
| institution | Directory Open Access Journal |
| issn | 2261-236X |
| language | English |
| last_indexed | 2024-12-19T16:16:35Z |
| publishDate | 2018-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | MATEC Web of Conferences |
| spelling | doaj.art-6a0f0d21efa14a83b9d396baaf61ae6b2022-12-21T20:14:36ZengEDP SciencesMATEC Web of Conferences2261-236X2018-01-011590200710.1051/matecconf/201815902007matecconf_ijcaet-isampe2018_02007Adomian decomposition method for solving initial value problems in vibration modelsMungkasi SudiEkaputra I Made WicaksanaA number of engineering problems have second-order ordinary differential equations as their mathematical models. In practice, we may have a large scale problem with a large number of degrees of freedom, which must be solved accurately. Therefore, treating the mathematical model governing the problems correctly is required in order to get an accurate solution. In this work, we use Adomian decomposition method to solve vibration models in the forms of initial value problems of second-order ordinary differential equations. However, for problems involving an external source, the Adomian decomposition method may not lead to an accurate solution if the external source is not correctly treated. In this paper, we propose a strategy to treat the external source when we implement the Adomian decomposition method to solve initial value problems of second-order ordinary differential equations. Computational results show that our strategy is indeed effective. We obtain accurate solutions to the considered problems. Note that exact solutions are often not available, so they need to be approximated using some methods, such as the Adomian decomposition method.https://doi.org/10.1051/matecconf/201815902007 |
| spellingShingle | Mungkasi Sudi Ekaputra I Made Wicaksana Adomian decomposition method for solving initial value problems in vibration models MATEC Web of Conferences |
| title | Adomian decomposition method for solving initial value problems in vibration models |
| title_full | Adomian decomposition method for solving initial value problems in vibration models |
| title_fullStr | Adomian decomposition method for solving initial value problems in vibration models |
| title_full_unstemmed | Adomian decomposition method for solving initial value problems in vibration models |
| title_short | Adomian decomposition method for solving initial value problems in vibration models |
| title_sort | adomian decomposition method for solving initial value problems in vibration models |
| url | https://doi.org/10.1051/matecconf/201815902007 |
| work_keys_str_mv | AT mungkasisudi adomiandecompositionmethodforsolvinginitialvalueproblemsinvibrationmodels AT ekaputraimadewicaksana adomiandecompositionmethodforsolvinginitialvalueproblemsinvibrationmodels |