Simulation of Ginzburg–Landau equation via rational RBF partition of unity approach.
Saved in:
| Title: | Simulation of Ginzburg–Landau equation via rational RBF partition of unity approach. |
|---|---|
| Authors: | Abbaszadeh, Mostafa1 (AUTHOR) m.abbaszadeh@aut.ac.ir, Salec, AliReza Bagheri2 (AUTHOR), Aal-Ezirej, Taghreed Abdul-Kareem Hatim2 (AUTHOR) |
| Source: | Optical & Quantum Electronics. Jan2024, Vol. 56 Issue 1, p1-18. 18p. |
| Subjects: | Radial basis functions, Partition of unity method, Collocation methods, Mathematical forms, Partial differential equations, Differential equations |
| Abstract: | In the recent decade, several numerical procedures are developed based on the radial basis functions (RBFs) in the strong and the weak form of the mathematical model. These numerical algorithms have been used to solve a wide range of differential equations. However, the accuracy of RBFs collocation method for some partial differential equations (PDEs) is low thus a modification of RBFs collocation plan is required. The main aim of the current paper is to employ an improvement of RBFs collocation algorithm i.e. rational RBFs (RRBFs) collocation method based on the partition of unity (PU) idea to get the numerical solution of the multi-dimensional Ginzburg–Landau equation. It is clear that the RBFs collocation approach is an important numerical procedure for solving PDEs in non-rectangular physical regions. For differential equations with sufficiently smooth solutions, the RBF collocation technique generates acceptable and efficient accuracy. The RBF collocation method may produce solutions with non-physical oscillations for the underlying functions which have steep gradients or discontinuities. Using a fourth-order time-split approach and rational RBFs (RRBFs) collocation method, a new numerical procedure is proposed. First, a fourth-order time-split approach is used to discrete the time variable. Then, a combination of RBFs-PU collocation technique has been developed to get a full-discrete scheme. At the end, several examples have been studied to show the stability, convergence, and accuracy of the proposed numerical algorithm. [ABSTRACT FROM AUTHOR] |
| Copyright of Optical & Quantum Electronics is the property of Springer Nature 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 |
|
Full text is not displayed to guests.
Login for full access.
|
|
| FullText | Links: – Type: pdflink Text: Availability: 1 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 174645126 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Simulation of Ginzburg–Landau equation via rational RBF partition of unity approach. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Abbaszadeh%2C+Mostafa%22">Abbaszadeh, Mostafa</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> m.abbaszadeh@aut.ac.ir</i><br /><searchLink fieldCode="AR" term="%22Salec%2C+AliReza+Bagheri%22">Salec, AliReza Bagheri</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Aal-Ezirej%2C+Taghreed+Abdul-Kareem+Hatim%22">Aal-Ezirej, Taghreed Abdul-Kareem Hatim</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Optical+%26+Quantum+Electronics%22">Optical & Quantum Electronics</searchLink>. Jan2024, Vol. 56 Issue 1, p1-18. 18p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Radial+basis+functions%22">Radial basis functions</searchLink><br /><searchLink fieldCode="DE" term="%22Partition+of+unity+method%22">Partition of unity method</searchLink><br /><searchLink fieldCode="DE" term="%22Collocation+methods%22">Collocation methods</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+forms%22">Mathematical forms</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In the recent decade, several numerical procedures are developed based on the radial basis functions (RBFs) in the strong and the weak form of the mathematical model. These numerical algorithms have been used to solve a wide range of differential equations. However, the accuracy of RBFs collocation method for some partial differential equations (PDEs) is low thus a modification of RBFs collocation plan is required. The main aim of the current paper is to employ an improvement of RBFs collocation algorithm i.e. rational RBFs (RRBFs) collocation method based on the partition of unity (PU) idea to get the numerical solution of the multi-dimensional Ginzburg–Landau equation. It is clear that the RBFs collocation approach is an important numerical procedure for solving PDEs in non-rectangular physical regions. For differential equations with sufficiently smooth solutions, the RBF collocation technique generates acceptable and efficient accuracy. The RBF collocation method may produce solutions with non-physical oscillations for the underlying functions which have steep gradients or discontinuities. Using a fourth-order time-split approach and rational RBFs (RRBFs) collocation method, a new numerical procedure is proposed. First, a fourth-order time-split approach is used to discrete the time variable. Then, a combination of RBFs-PU collocation technique has been developed to get a full-discrete scheme. At the end, several examples have been studied to show the stability, convergence, and accuracy of the proposed numerical algorithm. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Optical & Quantum Electronics is the property of Springer Nature 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=174645126 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s11082-023-05648-1 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 1 Subjects: – SubjectFull: Radial basis functions Type: general – SubjectFull: Partition of unity method Type: general – SubjectFull: Collocation methods Type: general – SubjectFull: Mathematical forms Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Differential equations Type: general Titles: – TitleFull: Simulation of Ginzburg–Landau equation via rational RBF partition of unity approach. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Abbaszadeh, Mostafa – PersonEntity: Name: NameFull: Salec, AliReza Bagheri – PersonEntity: Name: NameFull: Aal-Ezirej, Taghreed Abdul-Kareem Hatim IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 03068919 Numbering: – Type: volume Value: 56 – Type: issue Value: 1 Titles: – TitleFull: Optical & Quantum Electronics Type: main |
| ResultId | 1 |
