Accurate Four-Step Hybrid Block Method for Solving Higher-Order Initial Value Problems
This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid...
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| Format: | Article |
| Language: | Arabic |
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College of Science for Women, University of Baghdad
2022-08-01
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| Series: | Baghdad Science Journal |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5504 |
| _version_ | 1818015317542043648 |
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| author | Olanegan, O. O. Adeyefa, E. O. |
| author_facet | Olanegan, O. O. Adeyefa, E. O. |
| author_sort | Olanegan, O. O. |
| collection | DOAJ |
| description |
This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.
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| first_indexed | 2024-04-14T06:56:19Z |
| format | Article |
| id | doaj.art-a0fd4d1dce55481bbb608af7ed0696d4 |
| institution | Directory Open Access Journal |
| issn | 2078-8665 2411-7986 |
| language | Arabic |
| last_indexed | 2024-04-14T06:56:19Z |
| publishDate | 2022-08-01 |
| publisher | College of Science for Women, University of Baghdad |
| record_format | Article |
| series | Baghdad Science Journal |
| spelling | doaj.art-a0fd4d1dce55481bbb608af7ed0696d42022-12-22T02:06:53ZaraCollege of Science for Women, University of BaghdadBaghdad Science Journal2078-86652411-79862022-08-0119410.21123/bsj.2022.19.4.0787Accurate Four-Step Hybrid Block Method for Solving Higher-Order Initial Value ProblemsOlanegan, O. O.0Adeyefa, E. O.1Department of Mathematics, Federal University, Oye-Ekiti, Ekiti State, Nigeria.Department of Mathematics, Federal University, Oye-Ekiti, Ekiti State, Nigeria. This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5504Accuracy, Block Method, Convergence, Higher-Order, Initial Value Problems (IVPs), Ordinary Differential Equations, AMS Group: 65L05, 65L06, 65L10 |
| spellingShingle | Olanegan, O. O. Adeyefa, E. O. Accurate Four-Step Hybrid Block Method for Solving Higher-Order Initial Value Problems Baghdad Science Journal Accuracy, Block Method, Convergence, Higher-Order, Initial Value Problems (IVPs), Ordinary Differential Equations, AMS Group: 65L05, 65L06, 65L10 |
| title | Accurate Four-Step Hybrid Block Method for Solving Higher-Order Initial Value Problems |
| title_full | Accurate Four-Step Hybrid Block Method for Solving Higher-Order Initial Value Problems |
| title_fullStr | Accurate Four-Step Hybrid Block Method for Solving Higher-Order Initial Value Problems |
| title_full_unstemmed | Accurate Four-Step Hybrid Block Method for Solving Higher-Order Initial Value Problems |
| title_short | Accurate Four-Step Hybrid Block Method for Solving Higher-Order Initial Value Problems |
| title_sort | accurate four step hybrid block method for solving higher order initial value problems |
| topic | Accuracy, Block Method, Convergence, Higher-Order, Initial Value Problems (IVPs), Ordinary Differential Equations, AMS Group: 65L05, 65L06, 65L10 |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5504 |
| work_keys_str_mv | AT olaneganoo accuratefourstephybridblockmethodforsolvinghigherorderinitialvalueproblems AT adeyefaeo accuratefourstephybridblockmethodforsolvinghigherorderinitialvalueproblems |