An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations
This paper presented a linear multistep method for solving fourth order initial value problems of ordinary differential equations. Collocation and interpolation methods are adopted in the derivation of the new numerical scheme which is further applied to finding direct solution of fourth order ordi...
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| Format: | Article |
| Language: | English |
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Joint Coordination Centre of the World Bank assisted National Agricultural Research Programme (NARP)
2020-01-01
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| Series: | Journal of Applied Sciences and Environmental Management |
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| Online Access: | https://www.Ajol.Info/index.php/jasem/article/view/192550 |
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| author | B. Alechenu D.O. Oyewola |
| author_facet | B. Alechenu D.O. Oyewola |
| author_sort | B. Alechenu |
| collection | DOAJ |
| description |
This paper presented a linear multistep method for solving fourth order initial value problems of ordinary differential equations. Collocation and interpolation methods are adopted in the derivation of the new numerical scheme which is further applied to finding direct solution of fourth order ordinary differentiation equations. This implementation strategy is more accurate and efficient than Adams–Bashforth Method solution. The newly derive scheme have better stabilities properties than that of the Adams-Bashforth Method. Numerical examples are included to illustrate the reliability and accuracy of the new methods.
Keywords: Linear Multistep Methods, Region of Absolute Stability, Zero-Stability, Error Analysis, Collocation.
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| format | Article |
| id | doaj-art-bfc99da9117548e18eb2d1e9ab4fc1d1 |
| institution | Kabale University |
| issn | 2659-1502 2659-1499 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Joint Coordination Centre of the World Bank assisted National Agricultural Research Programme (NARP) |
| record_format | Article |
| series | Journal of Applied Sciences and Environmental Management |
| spelling | doaj-art-bfc99da9117548e18eb2d1e9ab4fc1d12025-02-08T19:51:22ZengJoint Coordination Centre of the World Bank assisted National Agricultural Research Programme (NARP)Journal of Applied Sciences and Environmental Management2659-15022659-14992020-01-012312An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential EquationsB. AlechenuD.O. Oyewola This paper presented a linear multistep method for solving fourth order initial value problems of ordinary differential equations. Collocation and interpolation methods are adopted in the derivation of the new numerical scheme which is further applied to finding direct solution of fourth order ordinary differentiation equations. This implementation strategy is more accurate and efficient than Adams–Bashforth Method solution. The newly derive scheme have better stabilities properties than that of the Adams-Bashforth Method. Numerical examples are included to illustrate the reliability and accuracy of the new methods. Keywords: Linear Multistep Methods, Region of Absolute Stability, Zero-Stability, Error Analysis, Collocation. https://www.Ajol.Info/index.php/jasem/article/view/192550Linear Multistep MethodsRegion of Absolute StabilityZero-StabilityError AnalysisCollocation |
| spellingShingle | B. Alechenu D.O. Oyewola An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations Journal of Applied Sciences and Environmental Management Linear Multistep Methods Region of Absolute Stability Zero-Stability Error Analysis Collocation |
| title | An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations |
| title_full | An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations |
| title_fullStr | An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations |
| title_full_unstemmed | An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations |
| title_short | An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations |
| title_sort | implicit collocation method for direct solution of fourth order ordinary differential equations |
| topic | Linear Multistep Methods Region of Absolute Stability Zero-Stability Error Analysis Collocation |
| url | https://www.Ajol.Info/index.php/jasem/article/view/192550 |
| work_keys_str_mv | AT balechenu animplicitcollocationmethodfordirectsolutionoffourthorderordinarydifferentialequations AT dooyewola animplicitcollocationmethodfordirectsolutionoffourthorderordinarydifferentialequations AT balechenu implicitcollocationmethodfordirectsolutionoffourthorderordinarydifferentialequations AT dooyewola implicitcollocationmethodfordirectsolutionoffourthorderordinarydifferentialequations |