Linear block method derived from Direct Taylor Series Expansions for solving linear third order boundary value problems
One of the conventional approaches for developing linear multistep method (LMM) for solving ordinary differential equations (ODEs) is the Taylor series expansions approach. Although this approach has not gained much attention in literature in comparison to its interpolation and numerical integration...
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| Format: | Article |
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American Scientific Publishers
2017
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| author | Adeyeye, Oluwaseun Omar, Zurni |
| author_facet | Adeyeye, Oluwaseun Omar, Zurni |
| author_sort | Adeyeye, Oluwaseun |
| collection | UUM |
| description | One of the conventional approaches for developing linear multistep method (LMM) for solving ordinary differential equations (ODEs) is the Taylor series expansions approach. Although this approach has not gained much attention in literature in comparison to its interpolation and numerical integration counterparts. The Taylor series expansions approach could also be adapted for developing linear block methods with the introduction of new required expressions to obtain the resulting block method. This linear block method directly approximates the numerical solution of third order ODEs without going through the rigour of reduction to a system of first order ODEs. Therefore, this article defines a general form of linear block methods for solving third order boundary value problems with the unknown coefficients in the block method obtained from direct Taylor series expansions. The basic properties of the resulting linear block method are investigated where the block method satisfies the convergence criteria. In addition, the linear block method is implemented to solve linear boundary value problems with better accuracy in comparison to other numerical approaches in literature. |
| first_indexed | 2024-07-04T06:36:53Z |
| format | Article |
| id | uum-27949 |
| institution | Universiti Utara Malaysia |
| last_indexed | 2024-07-04T06:36:53Z |
| publishDate | 2017 |
| publisher | American Scientific Publishers |
| record_format | eprints |
| spelling | uum-279492020-12-06T06:39:35Z https://repo.uum.edu.my/id/eprint/27949/ Linear block method derived from Direct Taylor Series Expansions for solving linear third order boundary value problems Adeyeye, Oluwaseun Omar, Zurni QA75 Electronic computers. Computer science One of the conventional approaches for developing linear multistep method (LMM) for solving ordinary differential equations (ODEs) is the Taylor series expansions approach. Although this approach has not gained much attention in literature in comparison to its interpolation and numerical integration counterparts. The Taylor series expansions approach could also be adapted for developing linear block methods with the introduction of new required expressions to obtain the resulting block method. This linear block method directly approximates the numerical solution of third order ODEs without going through the rigour of reduction to a system of first order ODEs. Therefore, this article defines a general form of linear block methods for solving third order boundary value problems with the unknown coefficients in the block method obtained from direct Taylor series expansions. The basic properties of the resulting linear block method are investigated where the block method satisfies the convergence criteria. In addition, the linear block method is implemented to solve linear boundary value problems with better accuracy in comparison to other numerical approaches in literature. American Scientific Publishers 2017 Article PeerReviewed Adeyeye, Oluwaseun and Omar, Zurni (2017) Linear block method derived from Direct Taylor Series Expansions for solving linear third order boundary value problems. Advanced Science, Engineering and Medicine, 9 (10). pp. 895-900. ISSN 2164-6627 http://doi.org/10.1166/asem.2017.2073 doi:10.1166/asem.2017.2073 doi:10.1166/asem.2017.2073 |
| spellingShingle | QA75 Electronic computers. Computer science Adeyeye, Oluwaseun Omar, Zurni Linear block method derived from Direct Taylor Series Expansions for solving linear third order boundary value problems |
| title | Linear block method derived from Direct Taylor Series Expansions for solving linear third order boundary value problems |
| title_full | Linear block method derived from Direct Taylor Series Expansions for solving linear third order boundary value problems |
| title_fullStr | Linear block method derived from Direct Taylor Series Expansions for solving linear third order boundary value problems |
| title_full_unstemmed | Linear block method derived from Direct Taylor Series Expansions for solving linear third order boundary value problems |
| title_short | Linear block method derived from Direct Taylor Series Expansions for solving linear third order boundary value problems |
| title_sort | linear block method derived from direct taylor series expansions for solving linear third order boundary value problems |
| topic | QA75 Electronic computers. Computer science |
| work_keys_str_mv | AT adeyeyeoluwaseun linearblockmethodderivedfromdirecttaylorseriesexpansionsforsolvinglinearthirdorderboundaryvalueproblems AT omarzurni linearblockmethodderivedfromdirecttaylorseriesexpansionsforsolvinglinearthirdorderboundaryvalueproblems |