The Reduction-to-First-Order Method and the Solution of Linear Constant-Coefficient Ordinary Differential Equations of Any Order.
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| Title: | The Reduction-to-First-Order Method and the Solution of Linear Constant-Coefficient Ordinary Differential Equations of Any Order. |
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| Authors: | Salim, Daniel1 daniel.salim@unpar.ac.id, Hoseana, Jonathan1 j.hoseana@unpar.ac.id |
| Source: | Engineering Letters. Dec2025, Vol. 33 Issue 12, p4777-4786. 10p. |
| Subjects: | Ordinary differential equations, Initial value problems, Differential equations, Signal convolution |
| Abstract: | The article focuses on the reduction-to-first-order method for solving linear constant-coefficient ordinary differential equations (ODEs) of any order. It presents explicit formulas for the general solution and the corresponding initial value problem, addressing both homogeneous and non-homogeneous cases without requiring separate treatments for equal characteristic roots. The authors introduce key concepts such as convolution and an indefinite variant to streamline the solution process. The paper aims to provide a rigorous theoretical foundation for this method, which has been previously underexplored in the literature. [Extracted from the article] |
| Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) 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: 189696730 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The Reduction-to-First-Order Method and the Solution of Linear Constant-Coefficient Ordinary Differential Equations of Any Order. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Salim%2C+Daniel%22">Salim, Daniel</searchLink><relatesTo>1</relatesTo><i> daniel.salim@unpar.ac.id</i><br /><searchLink fieldCode="AR" term="%22Hoseana%2C+Jonathan%22">Hoseana, Jonathan</searchLink><relatesTo>1</relatesTo><i> j.hoseana@unpar.ac.id</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Engineering+Letters%22">Engineering Letters</searchLink>. Dec2025, Vol. 33 Issue 12, p4777-4786. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Ordinary+differential+equations%22">Ordinary differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Initial+value+problems%22">Initial value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Signal+convolution%22">Signal convolution</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The article focuses on the reduction-to-first-order method for solving linear constant-coefficient ordinary differential equations (ODEs) of any order. It presents explicit formulas for the general solution and the corresponding initial value problem, addressing both homogeneous and non-homogeneous cases without requiring separate treatments for equal characteristic roots. The authors introduce key concepts such as convolution and an indefinite variant to streamline the solution process. The paper aims to provide a rigorous theoretical foundation for this method, which has been previously underexplored in the literature. [Extracted from the article] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Engineering Letters is the property of International Association of Engineers (IAENG) 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=189696730 |
| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 4777 Subjects: – SubjectFull: Ordinary differential equations Type: general – SubjectFull: Initial value problems Type: general – SubjectFull: Differential equations Type: general – SubjectFull: Signal convolution Type: general Titles: – TitleFull: The Reduction-to-First-Order Method and the Solution of Linear Constant-Coefficient Ordinary Differential Equations of Any Order. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Salim, Daniel – PersonEntity: Name: NameFull: Hoseana, Jonathan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 1816093X Numbering: – Type: volume Value: 33 – Type: issue Value: 12 Titles: – TitleFull: Engineering Letters Type: main |
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