Academic Journal
Stability analysis and L1-finite difference modeling of inverse problems for fractional Schrödinger equations with variable diffusion.
| Τίτλος: | Stability analysis and L1-finite difference modeling of inverse problems for fractional Schrödinger equations with variable diffusion. |
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| Συγγραφείς: | Huntul, Mousa J., Modanli, Mahmut, Izadi, Mohammad |
| Πηγή: | AIMS Mathematics; 2026, Vol. 11 Issue 3, p1-24, 24p |
| Θεματικοί όροι: | Finite difference method, Caputo fractional derivatives, Diffusion coefficients, Stability theory, Partial differential equations, Inverse problems, Numerical analysis |
| Περίληψη: | This study developed a finite difference method (FDM) for a time-fractional inverse problem associated with Schrödinger partial differential equations. The main objective of the inverse problem is the simultaneous identification of the unknown source function p (x) and the state variable w (t , x). The mathematical model involves the Caputo fractional order derivative (CFOD) of order 0 < α ≤ 1 and incorporates a spatially variable diffusion coefficient a (x) , which significantly increases the complexity of the problem compared with constant-coefficient models. Homogeneous Dirichlet boundary value conditions (DBVCs) were imposed on the spatial domain. For the numerical discretization, the time-CFOD was approximated using a consistent L1-type scheme, while the spatial derivatives were discretized by second-order central finite difference schemes (FDSs). Stability estimates and convergence properties of the proposed numerical scheme are rigorously established using discrete energy techniques. The analysis shows that the method achieves a convergence order of O (τ 2 − α + h 2). To validate the theoretical results, numerical experiments were performed for two benchmark problems with diffusion coefficients a (x) = x 2 + 1 and a (x) = x 3 + 1. The obtained numerical results confirm the effectiveness and robustness of the proposed approach. Graphical comparisons illustrate the behavior of solutions for different fractional orders as time evolves, while error tables demonstrate that the fractional-order solutions provide more accurate approximations to the exact solution than the corresponding integer-order case. [ABSTRACT FROM AUTHOR] |
| Copyright of AIMS Mathematics is the property of American Institute of Mathematical Sciences 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.) | |
| Βάση Δεδομένων: | Complementary Index |
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| Header | DbId: edb DbLabel: Complementary Index An: 192838975 RelevancyScore: 1061 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1060.7568359375 |
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| Items | – Name: Title Label: Title Group: Ti Data: Stability analysis and L1-finite difference modeling of inverse problems for fractional Schrödinger equations with variable diffusion. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Huntul%2C+Mousa+J%2E%22">Huntul, Mousa J.</searchLink><br /><searchLink fieldCode="AR" term="%22Modanli%2C+Mahmut%22">Modanli, Mahmut</searchLink><br /><searchLink fieldCode="AR" term="%22Izadi%2C+Mohammad%22">Izadi, Mohammad</searchLink> – Name: TitleSource Label: Source Group: Src Data: AIMS Mathematics; 2026, Vol. 11 Issue 3, p1-24, 24p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink><br /><searchLink fieldCode="DE" term="%22Caputo+fractional+derivatives%22">Caputo fractional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Diffusion+coefficients%22">Diffusion coefficients</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+problems%22">Inverse problems</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study developed a finite difference method (FDM) for a time-fractional inverse problem associated with Schrödinger partial differential equations. The main objective of the inverse problem is the simultaneous identification of the unknown source function p (x) and the state variable w (t , x). The mathematical model involves the Caputo fractional order derivative (CFOD) of order 0 < α ≤ 1 and incorporates a spatially variable diffusion coefficient a (x) , which significantly increases the complexity of the problem compared with constant-coefficient models. Homogeneous Dirichlet boundary value conditions (DBVCs) were imposed on the spatial domain. For the numerical discretization, the time-CFOD was approximated using a consistent L1-type scheme, while the spatial derivatives were discretized by second-order central finite difference schemes (FDSs). Stability estimates and convergence properties of the proposed numerical scheme are rigorously established using discrete energy techniques. The analysis shows that the method achieves a convergence order of O (τ 2 − α + h 2). To validate the theoretical results, numerical experiments were performed for two benchmark problems with diffusion coefficients a (x) = x 2 + 1 and a (x) = x 3 + 1. The obtained numerical results confirm the effectiveness and robustness of the proposed approach. Graphical comparisons illustrate the behavior of solutions for different fractional orders as time evolves, while error tables demonstrate that the fractional-order solutions provide more accurate approximations to the exact solution than the corresponding integer-order case. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of AIMS Mathematics is the property of American Institute of Mathematical Sciences 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: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 1 Subjects: – SubjectFull: Finite difference method Type: general – SubjectFull: Caputo fractional derivatives Type: general – SubjectFull: Diffusion coefficients Type: general – SubjectFull: Stability theory Type: general – SubjectFull: Partial differential equations Type: general – SubjectFull: Inverse problems Type: general – SubjectFull: Numerical analysis Type: general Titles: – TitleFull: Stability analysis and L1-finite difference modeling of inverse problems for fractional Schrödinger equations with variable diffusion. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Huntul, Mousa J. – PersonEntity: Name: NameFull: Modanli, Mahmut – PersonEntity: Name: NameFull: Izadi, Mohammad IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 24736988 Numbering: – Type: volume Value: 11 – Type: issue Value: 3 Titles: – TitleFull: AIMS Mathematics Type: main |
| ResultId | 1 |