Uniform numerical method for singularly perturbed parabolic time delay reaction-diffusion problems arising in control theory.
Saved in:
| Title: | Uniform numerical method for singularly perturbed parabolic time delay reaction-diffusion problems arising in control theory. |
|---|---|
| Authors: | Huntul, Mousa J.1, Daba, Imiru Takele2 imirutakele@gmail.com |
| Source: | Mathematical Modelling & Analysis. 2026, Vol. 31 Issue 3, p392-406. 15p. |
| Subjects: | Singular perturbations, Reaction-diffusion equations, Finite difference method, Numerical analysis, Stability criterion, Crank-Nicolson method, Parabolic differential equations |
| Abstract: | This paper introduces a uniform numerical scheme to find approximate solutions for singularly perturbed parabolic time delay reaction-diffusion problems. The scheme utilizes the Crank-Nicolson method for approximating time derivatives, combined with a novel finite difference method for spatial discretization. The stability and uniform convergence of the proposed scheme are investigated. The primary objective of this work is to demonstrate that the proposed scheme achieves a parameter-free error bound of order O(k2 + N-2). To validate the theoretical results, various numerical experiments have been conducted, showing that the proposed scheme yields superior results compared to some existing methods in the literature. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical University 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 | Links: – Type: pdflink Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 194823830 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Uniform numerical method for singularly perturbed parabolic time delay reaction-diffusion problems arising in control theory. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Huntul%2C+Mousa+J%2E%22">Huntul, Mousa J.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Daba%2C+Imiru+Takele%22">Daba, Imiru Takele</searchLink><relatesTo>2</relatesTo><i> imirutakele@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+Modelling+%26+Analysis%22">Mathematical Modelling & Analysis</searchLink>. 2026, Vol. 31 Issue 3, p392-406. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Singular+perturbations%22">Singular perturbations</searchLink><br /><searchLink fieldCode="DE" term="%22Reaction-diffusion+equations%22">Reaction-diffusion equations</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+criterion%22">Stability criterion</searchLink><br /><searchLink fieldCode="DE" term="%22Crank-Nicolson+method%22">Crank-Nicolson method</searchLink><br /><searchLink fieldCode="DE" term="%22Parabolic+differential+equations%22">Parabolic differential equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper introduces a uniform numerical scheme to find approximate solutions for singularly perturbed parabolic time delay reaction-diffusion problems. The scheme utilizes the Crank-Nicolson method for approximating time derivatives, combined with a novel finite difference method for spatial discretization. The stability and uniform convergence of the proposed scheme are investigated. The primary objective of this work is to demonstrate that the proposed scheme achieves a parameter-free error bound of order O(k2 + N-2). To validate the theoretical results, various numerical experiments have been conducted, showing that the proposed scheme yields superior results compared to some existing methods in the literature. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical University 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=194823830 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3846/mma.2026.24165 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 392 Subjects: – SubjectFull: Singular perturbations Type: general – SubjectFull: Reaction-diffusion equations Type: general – SubjectFull: Finite difference method Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Stability criterion Type: general – SubjectFull: Crank-Nicolson method Type: general – SubjectFull: Parabolic differential equations Type: general Titles: – TitleFull: Uniform numerical method for singularly perturbed parabolic time delay reaction-diffusion problems arising in control theory. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Huntul, Mousa J. – PersonEntity: Name: NameFull: Daba, Imiru Takele IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13926292 Numbering: – Type: volume Value: 31 – Type: issue Value: 3 Titles: – TitleFull: Mathematical Modelling & Analysis Type: main |
| ResultId | 1 |
