Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains
We consider fractional mathematical models of fluid-porous interfaces in channel geometry. This provokes us to deal with numerical identification of the external boundary conditions for 1D and 2D time fractional parabolic problems on disjoint domains. First, we discuss the time discretization, then...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/4/326 |
| _version_ | 1827745022305370112 |
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| author | Miglena N. Koleva Lubin G. Vulkov |
| author_facet | Miglena N. Koleva Lubin G. Vulkov |
| author_sort | Miglena N. Koleva |
| collection | DOAJ |
| description | We consider fractional mathematical models of fluid-porous interfaces in channel geometry. This provokes us to deal with numerical identification of the external boundary conditions for 1D and 2D time fractional parabolic problems on disjoint domains. First, we discuss the time discretization, then we decouple the full inverse problem into two Dirichlet problems at each time level. On this base, we develop decomposition techniques to obtain exact formulas for the unknown boundary conditions at point measurements. A discrete version of the analytical approach is realized on time adaptive mesh for different fractional order of the equations in each of the disjoint domains. A variety of numerical examples are discussed. |
| first_indexed | 2024-03-11T05:00:15Z |
| format | Article |
| id | doaj.art-9486d2106f464104aec91e06af6ae349 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T05:00:15Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-9486d2106f464104aec91e06af6ae3492023-11-17T19:19:37ZengMDPI AGFractal and Fractional2504-31102023-04-017432610.3390/fractalfract7040326Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint DomainsMiglena N. Koleva0Lubin G. Vulkov1Department of Mathematics, Faculty of Natural Sciences and Education, University of Ruse “Angel Kanchev”, 7017 Ruse, BulgariaDepartment of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse “Angel Kanchev”, 7017 Ruse, BulgariaWe consider fractional mathematical models of fluid-porous interfaces in channel geometry. This provokes us to deal with numerical identification of the external boundary conditions for 1D and 2D time fractional parabolic problems on disjoint domains. First, we discuss the time discretization, then we decouple the full inverse problem into two Dirichlet problems at each time level. On this base, we develop decomposition techniques to obtain exact formulas for the unknown boundary conditions at point measurements. A discrete version of the analytical approach is realized on time adaptive mesh for different fractional order of the equations in each of the disjoint domains. A variety of numerical examples are discussed.https://www.mdpi.com/2504-3110/7/4/326Caputo fractional derivativeproblems on disjoint domainsinverse problemsexternal boundary conditionsdifference scheme |
| spellingShingle | Miglena N. Koleva Lubin G. Vulkov Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains Fractal and Fractional Caputo fractional derivative problems on disjoint domains inverse problems external boundary conditions difference scheme |
| title | Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains |
| title_full | Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains |
| title_fullStr | Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains |
| title_full_unstemmed | Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains |
| title_short | Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains |
| title_sort | numerical identification of external boundary conditions for time fractional parabolic equations on disjoint domains |
| topic | Caputo fractional derivative problems on disjoint domains inverse problems external boundary conditions difference scheme |
| url | https://www.mdpi.com/2504-3110/7/4/326 |
| work_keys_str_mv | AT miglenankoleva numericalidentificationofexternalboundaryconditionsfortimefractionalparabolicequationsondisjointdomains AT lubingvulkov numericalidentificationofexternalboundaryconditionsfortimefractionalparabolicequationsondisjointdomains |