Second derivative numerical differentiation formulas for stiff systems of ODEs.
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| Title: | Second derivative numerical differentiation formulas for stiff systems of ODEs. |
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| Authors: | Hojjati, G.1,2 (AUTHOR) ghojjati@tabrizu.ac.ir, Abdi, A.1,2 (AUTHOR) a_abdi@tabrizu.ac.ir, Conte, D.3 (AUTHOR) dajconte@unisa.it |
| Source: | Applied Numerical Mathematics. Aug2026, Vol. 226, p119-127. 9p. |
| Subjects: | Numerical differentiation, Ordinary differential equations, Stability theory, Initial value problems, Approximation error, Numerical solutions to differential equations, Numerical analysis |
| Abstract: | The SDBDF methods, which extend BDF methods by incorporating the second derivative of the solution, have attracted interest due to their favorable convergence and stability properties. Inspired by the approach used in developing numerical differentiation formulas for solving stiff ODEs—those employed in Matlab 's ode15s solver—this paper proposes a modification to the SDBDF methods that reduces the local truncation error, with only a slight loss of stability in higher-order cases. The analysis of the newly designed methods demonstrates their capability and efficiency in solving stiff initial value problems for ordinary differential equations. Numerical experiments on several well-known stiff problems confirm the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193590481 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Second derivative numerical differentiation formulas for stiff systems of ODEs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hojjati%2C+G%2E%22">Hojjati, G.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> ghojjati@tabrizu.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Abdi%2C+A%2E%22">Abdi, A.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> a_abdi@tabrizu.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Conte%2C+D%2E%22">Conte, D.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> dajconte@unisa.it</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Aug2026, Vol. 226, p119-127. 9p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Numerical+differentiation%22">Numerical differentiation</searchLink><br /><searchLink fieldCode="DE" term="%22Ordinary+differential+equations%22">Ordinary differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Initial+value+problems%22">Initial value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+differential+equations%22">Numerical solutions to differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The SDBDF methods, which extend BDF methods by incorporating the second derivative of the solution, have attracted interest due to their favorable convergence and stability properties. Inspired by the approach used in developing numerical differentiation formulas for solving stiff ODEs—those employed in Matlab 's ode15s solver—this paper proposes a modification to the SDBDF methods that reduces the local truncation error, with only a slight loss of stability in higher-order cases. The analysis of the newly designed methods demonstrates their capability and efficiency in solving stiff initial value problems for ordinary differential equations. Numerical experiments on several well-known stiff problems confirm the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. 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: 10.1016/j.apnum.2026.04.002 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 9 StartPage: 119 Subjects: – SubjectFull: Numerical differentiation Type: general – SubjectFull: Ordinary differential equations Type: general – SubjectFull: Stability theory Type: general – SubjectFull: Initial value problems Type: general – SubjectFull: Approximation error Type: general – SubjectFull: Numerical solutions to differential equations Type: general – SubjectFull: Numerical analysis Type: general Titles: – TitleFull: Second derivative numerical differentiation formulas for stiff systems of ODEs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hojjati, G. – PersonEntity: Name: NameFull: Abdi, A. – PersonEntity: Name: NameFull: Conte, D. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 01689274 Numbering: – Type: volume Value: 226 Titles: – TitleFull: Applied Numerical Mathematics Type: main |
| ResultId | 1 |
