An Overlapping One‐Step Multiderivative Hybrid Block Method for Solving Second‐Order Initial Value Problems.
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| Title: | An Overlapping One‐Step Multiderivative Hybrid Block Method for Solving Second‐Order Initial Value Problems. |
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| Authors: | Rufai, Uthman O.1 (AUTHOR) rufaiuthman18@gmail.com, Sibanda, Precious1 (AUTHOR), Goqo, Sicelo P.1 (AUTHOR), Motsa, Sandile1 (AUTHOR), Simos, Theodore1 (AUTHOR) tsimos.conf@gmail.com |
| Source: | Journal of Applied Mathematics. 1/29/2026, Vol. 2026, p1-18. 18p. |
| Subjects: | Initial value problems, Numerical analysis, Stability (Mechanics), Error analysis in mathematics, Iterative methods (Mathematics) |
| Abstract: | This paper presents a one‐step multiderivative hybrid block method of Order 12 that incorporates an overlapping strategy, in which intrastep points from the previous block are reused in the current step to enhance accuracy and stability when solving linear and nonlinear initial value problems. The derivation incorporates a multistep collocation and interpolation technique, using power series as the basis function for the approximate solution. Within a one‐step block, three intrastep points are considered. As a foundational step, a non‐overlapping one‐step multiderivative scheme is first developed and expressed in matrix form. The overlapping aspect of the method is then introduced by incorporating the second‐to‐last intrastep point of the previous step into each integrating block. The accuracy, consistency, and stability properties of the method are analyzed. The features of the method are determined through an error analysis of the numerical solutions of linear and nonlinear second‐order initial value problems. The nonlinear initial value problems are converted into linear ones using a modified Picard iteration technique. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method. The results are evaluated against other methods from the literature. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 194047037 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: An Overlapping One‐Step Multiderivative Hybrid Block Method for Solving Second‐Order Initial Value Problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Rufai%2C+Uthman+O%2E%22">Rufai, Uthman O.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rufaiuthman18@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Sibanda%2C+Precious%22">Sibanda, Precious</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Goqo%2C+Sicelo+P%2E%22">Goqo, Sicelo P.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Motsa%2C+Sandile%22">Motsa, Sandile</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Simos%2C+Theodore%22">Simos, Theodore</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> tsimos.conf@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 1/29/2026, Vol. 2026, p1-18. 18p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Initial+value+problems%22">Initial value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+%28Mechanics%29%22">Stability (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Error+analysis+in+mathematics%22">Error analysis in mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper presents a one‐step multiderivative hybrid block method of Order 12 that incorporates an overlapping strategy, in which intrastep points from the previous block are reused in the current step to enhance accuracy and stability when solving linear and nonlinear initial value problems. The derivation incorporates a multistep collocation and interpolation technique, using power series as the basis function for the approximate solution. Within a one‐step block, three intrastep points are considered. As a foundational step, a non‐overlapping one‐step multiderivative scheme is first developed and expressed in matrix form. The overlapping aspect of the method is then introduced by incorporating the second‐to‐last intrastep point of the previous step into each integrating block. The accuracy, consistency, and stability properties of the method are analyzed. The features of the method are determined through an error analysis of the numerical solutions of linear and nonlinear second‐order initial value problems. The nonlinear initial value problems are converted into linear ones using a modified Picard iteration technique. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method. The results are evaluated against other methods from the literature. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1155/jama/9948007 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 1 Subjects: – SubjectFull: Initial value problems Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Stability (Mechanics) Type: general – SubjectFull: Error analysis in mathematics Type: general – SubjectFull: Iterative methods (Mathematics) Type: general Titles: – TitleFull: An Overlapping One‐Step Multiderivative Hybrid Block Method for Solving Second‐Order Initial Value Problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Rufai, Uthman O. – PersonEntity: Name: NameFull: Sibanda, Precious – PersonEntity: Name: NameFull: Goqo, Sicelo P. – PersonEntity: Name: NameFull: Motsa, Sandile – PersonEntity: Name: NameFull: Simos, Theodore IsPartOfRelationships: – BibEntity: Dates: – D: 29 M: 01 Text: 1/29/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 1110757X Numbering: – Type: volume Value: 2026 Titles: – TitleFull: Journal of Applied Mathematics Type: main |
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