Numerical Identification of Boundary Conditions for Richards’ Equation
A time stepping quasilinearization approach to the mixed (or coupled) form of one and two dimensional Richards’ equations is developed. For numerical solution of the linear ordinary differential equation (ODE) for 1D case and elliptic for 2D case, obtained after this semidiscretization, a finite vol...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/2/299 |
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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 | A time stepping quasilinearization approach to the mixed (or coupled) form of one and two dimensional Richards’ equations is developed. For numerical solution of the linear ordinary differential equation (ODE) for 1D case and elliptic for 2D case, obtained after this semidiscretization, a finite volume method is used for direct problems arising on each time level. Next, we propose a version of the decomposition method for the numerical solution of the inverse ODE and 2D elliptic boundary problems. Computational results for some soil types and its related parameters reported in the literature are presented. |
| first_indexed | 2024-03-08T10:42:46Z |
| format | Article |
| id | doaj.art-e95ad7b4d2e04dd8a9368ab159776105 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T10:42:46Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e95ad7b4d2e04dd8a9368ab1597761052024-01-26T17:33:11ZengMDPI AGMathematics2227-73902024-01-0112229910.3390/math12020299Numerical Identification of Boundary Conditions for Richards’ EquationMiglena N. Koleva0Lubin G. Vulkov1Department of Mathematics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Street, 7017 Ruse, BulgariaDepartment of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Street, 7017 Ruse, BulgariaA time stepping quasilinearization approach to the mixed (or coupled) form of one and two dimensional Richards’ equations is developed. For numerical solution of the linear ordinary differential equation (ODE) for 1D case and elliptic for 2D case, obtained after this semidiscretization, a finite volume method is used for direct problems arising on each time level. Next, we propose a version of the decomposition method for the numerical solution of the inverse ODE and 2D elliptic boundary problems. Computational results for some soil types and its related parameters reported in the literature are presented.https://www.mdpi.com/2227-7390/12/2/299soil-water flowRichards’ equationinverse boundary condition problemODE systemBellman-Kalaba quasilinearizationdecomposition of the solution |
| spellingShingle | Miglena N. Koleva Lubin G. Vulkov Numerical Identification of Boundary Conditions for Richards’ Equation Mathematics soil-water flow Richards’ equation inverse boundary condition problem ODE system Bellman-Kalaba quasilinearization decomposition of the solution |
| title | Numerical Identification of Boundary Conditions for Richards’ Equation |
| title_full | Numerical Identification of Boundary Conditions for Richards’ Equation |
| title_fullStr | Numerical Identification of Boundary Conditions for Richards’ Equation |
| title_full_unstemmed | Numerical Identification of Boundary Conditions for Richards’ Equation |
| title_short | Numerical Identification of Boundary Conditions for Richards’ Equation |
| title_sort | numerical identification of boundary conditions for richards equation |
| topic | soil-water flow Richards’ equation inverse boundary condition problem ODE system Bellman-Kalaba quasilinearization decomposition of the solution |
| url | https://www.mdpi.com/2227-7390/12/2/299 |
| work_keys_str_mv | AT miglenankoleva numericalidentificationofboundaryconditionsforrichardsequation AT lubingvulkov numericalidentificationofboundaryconditionsforrichardsequation |