Generalization of a class of uniformly optimized k-step hybrid block method for solving two-point boundary value problems
This study aims to develop, analyze and implement an efficient method for approximating two-point boundary value problems of ordinary differential equations. The method contains six and twelve implicit formulas, respectively, for the one-step and two-step schemes. The continuous approximations, usin...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-01-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722007616 |
| _version_ | 1797950759224999936 |
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| author | Muideen O. Ogunniran Gabriel C. Olaleye Omotayo A. Taiwo Ali Shokri Kamsing Nonlaopon |
| author_facet | Muideen O. Ogunniran Gabriel C. Olaleye Omotayo A. Taiwo Ali Shokri Kamsing Nonlaopon |
| author_sort | Muideen O. Ogunniran |
| collection | DOAJ |
| description | This study aims to develop, analyze and implement an efficient method for approximating two-point boundary value problems of ordinary differential equations. The method contains six and twelve implicit formulas, respectively, for the one-step and two-step schemes. The continuous approximations, using the shifted Chebyshev polynomial as the basis function, were obtained via evaluations at three different points on the selected one-step method, including two optimized hybrid points. Evaluations were carried out on six different points on the selected two-step method, including four generalized optimized hybrid points. Qualitative analysis of the method proves the proposed methods are consistent, zero-stable, convergent and have a larger region of absolute stability. The quantitative analysis shows that the methods compared favorably well and established some superiority strength with the existing methods. |
| first_indexed | 2024-04-10T22:20:13Z |
| format | Article |
| id | doaj.art-cadb6e49ff71458a944d48579bc26db7 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-10T22:20:13Z |
| publishDate | 2023-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-cadb6e49ff71458a944d48579bc26db72023-01-18T04:30:33ZengElsevierResults in Physics2211-37972023-01-0144106147Generalization of a class of uniformly optimized k-step hybrid block method for solving two-point boundary value problemsMuideen O. Ogunniran0Gabriel C. Olaleye1Omotayo A. Taiwo2Ali Shokri3Kamsing Nonlaopon4Department of Mathematical Sciences, Osun State University, Osogbo, +234, NigeriaDepartment of Mathematics, University of Ilorin, Ilorin, +234, NigeriaDepartment of Mathematics, University of Ilorin, Ilorin, +234, NigeriaDepartment of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh 83111-55181, IranDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand; Corresponding author.This study aims to develop, analyze and implement an efficient method for approximating two-point boundary value problems of ordinary differential equations. The method contains six and twelve implicit formulas, respectively, for the one-step and two-step schemes. The continuous approximations, using the shifted Chebyshev polynomial as the basis function, were obtained via evaluations at three different points on the selected one-step method, including two optimized hybrid points. Evaluations were carried out on six different points on the selected two-step method, including four generalized optimized hybrid points. Qualitative analysis of the method proves the proposed methods are consistent, zero-stable, convergent and have a larger region of absolute stability. The quantitative analysis shows that the methods compared favorably well and established some superiority strength with the existing methods.http://www.sciencedirect.com/science/article/pii/S2211379722007616Hybrid pointsTwo-point bvpsk-step hybrid block methodsZero-stabilityStabilityOptimization |
| spellingShingle | Muideen O. Ogunniran Gabriel C. Olaleye Omotayo A. Taiwo Ali Shokri Kamsing Nonlaopon Generalization of a class of uniformly optimized k-step hybrid block method for solving two-point boundary value problems Results in Physics Hybrid points Two-point bvps k-step hybrid block methods Zero-stability Stability Optimization |
| title | Generalization of a class of uniformly optimized k-step hybrid block method for solving two-point boundary value problems |
| title_full | Generalization of a class of uniformly optimized k-step hybrid block method for solving two-point boundary value problems |
| title_fullStr | Generalization of a class of uniformly optimized k-step hybrid block method for solving two-point boundary value problems |
| title_full_unstemmed | Generalization of a class of uniformly optimized k-step hybrid block method for solving two-point boundary value problems |
| title_short | Generalization of a class of uniformly optimized k-step hybrid block method for solving two-point boundary value problems |
| title_sort | generalization of a class of uniformly optimized k step hybrid block method for solving two point boundary value problems |
| topic | Hybrid points Two-point bvps k-step hybrid block methods Zero-stability Stability Optimization |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722007616 |
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