IRK-WSGD methods for space fractional diffusion equations.
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| Title: | IRK-WSGD methods for space fractional diffusion equations. |
|---|---|
| Authors: | Lin, Fu-Rong1 (AUTHOR) frlin@stu.edu.cn, Qiu, Yi-Feng1 (AUTHOR), She, Zi-Hang1,2 (AUTHOR) |
| Source: | Applied Numerical Mathematics. Jun2021, Vol. 164, p222-244. 23p. |
| Subjects: | Heat equation, Initial value problems, Ordinary differential equations, Linear systems |
| Abstract: | In this paper, we develop high order numerical schemes for the solution of the initial-boundary value problem of one-dimensional and two-dimensional space fractional diffusion equations of orders belonging to the interval (1 , 2). Firstly, certain weighted and shifted Grünwald difference (WSGD) operator is used to approximate space Riemann-Liouville fractional derivatives, resulting in a linear system of ordinary differential equations (ODEs). Then an implicit Runge-Kutta (IRK) method is applied to discretize the resulted ODEs. Thus, we get an IRK-WSGD method for the fractional diffusion equation. We prove that under certain hypotheses, the proposed IRK-WSGD schemes are stable and have temporally fourth order accuracy and spatially second/third order accuracy. Preconditioning for discretization linear systems is discussed. Numerical experiments are presented to illustrate the accuracy and efficiency of the method. [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: 148432314 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: IRK-WSGD methods for space fractional diffusion equations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lin%2C+Fu-Rong%22">Lin, Fu-Rong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> frlin@stu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Qiu%2C+Yi-Feng%22">Qiu, Yi-Feng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22She%2C+Zi-Hang%22">She, Zi-Hang</searchLink><relatesTo>1,2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Jun2021, Vol. 164, p222-244. 23p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Heat+equation%22">Heat equation</searchLink><br /><searchLink fieldCode="DE" term="%22Initial+value+problems%22">Initial value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Ordinary+differential+equations%22">Ordinary differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we develop high order numerical schemes for the solution of the initial-boundary value problem of one-dimensional and two-dimensional space fractional diffusion equations of orders belonging to the interval (1 , 2). Firstly, certain weighted and shifted Grünwald difference (WSGD) operator is used to approximate space Riemann-Liouville fractional derivatives, resulting in a linear system of ordinary differential equations (ODEs). Then an implicit Runge-Kutta (IRK) method is applied to discretize the resulted ODEs. Thus, we get an IRK-WSGD method for the fractional diffusion equation. We prove that under certain hypotheses, the proposed IRK-WSGD schemes are stable and have temporally fourth order accuracy and spatially second/third order accuracy. Preconditioning for discretization linear systems is discussed. Numerical experiments are presented to illustrate the accuracy and efficiency of the method. [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.2020.11.012 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 23 StartPage: 222 Subjects: – SubjectFull: Heat equation Type: general – SubjectFull: Initial value problems Type: general – SubjectFull: Ordinary differential equations Type: general – SubjectFull: Linear systems Type: general Titles: – TitleFull: IRK-WSGD methods for space fractional diffusion equations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lin, Fu-Rong – PersonEntity: Name: NameFull: Qiu, Yi-Feng – PersonEntity: Name: NameFull: She, Zi-Hang IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 01689274 Numbering: – Type: volume Value: 164 Titles: – TitleFull: Applied Numerical Mathematics Type: main |
| ResultId | 1 |
