Inverse Problem Numerical Analysis of Forager Bee Losses in Spatial Environment without Contamination
We consider an inverse problem of recovering the mortality rate in the honey bee difference equation model, that tracks a forage honeybee leaving and entering the hive each day. We concentrate our analysis to the model without pesticide contamination in the symmetric spatial environment. Thus, the m...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/12/2099 |
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| author | Atanas Z. Atanasov Miglena N. Koleva Lubin G. Vulkov |
| author_facet | Atanas Z. Atanasov Miglena N. Koleva Lubin G. Vulkov |
| author_sort | Atanas Z. Atanasov |
| collection | DOAJ |
| description | We consider an inverse problem of recovering the mortality rate in the honey bee difference equation model, that tracks a forage honeybee leaving and entering the hive each day. We concentrate our analysis to the model without pesticide contamination in the symmetric spatial environment. Thus, the mathematical problem is formulated as a symmetric inverse problem for reaction coefficient at final time constraint. We use the overspecified information to transform the inverse coefficient problem to the forward problem with non-local terms in the differential operator and the initial condition. First, we apply semidiscretization in space to the new nonsymmetric differential operator. Then, the resulting non-local nonsymmetric system of ordinary differential equations (ODEs) is discretized by three iterative numerical schemes using different time stepping. Results of numerical experiments which compare the efficiency of the numerical schemes are discussed. Results from numerical tests with synthetic and real data are presented and discussed, as well. |
| first_indexed | 2024-03-08T20:20:02Z |
| format | Article |
| id | doaj.art-6f5f4c36f3f347d781305cb5c2605397 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-08T20:20:02Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-6f5f4c36f3f347d781305cb5c26053972023-12-22T14:45:03ZengMDPI AGSymmetry2073-89942023-11-011512209910.3390/sym15122099Inverse Problem Numerical Analysis of Forager Bee Losses in Spatial Environment without ContaminationAtanas Z. Atanasov0Miglena N. Koleva1Lubin G. Vulkov2Agricultural Machinery Department, Agrarian and Industrial Faculty, University of Ruse, 8 Studentska Str., 7017 Ruse, BulgariaDepartment of Mathematics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Str., 7017 Ruse, BulgariaDepartment of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Str., 7017 Ruse, BulgariaWe consider an inverse problem of recovering the mortality rate in the honey bee difference equation model, that tracks a forage honeybee leaving and entering the hive each day. We concentrate our analysis to the model without pesticide contamination in the symmetric spatial environment. Thus, the mathematical problem is formulated as a symmetric inverse problem for reaction coefficient at final time constraint. We use the overspecified information to transform the inverse coefficient problem to the forward problem with non-local terms in the differential operator and the initial condition. First, we apply semidiscretization in space to the new nonsymmetric differential operator. Then, the resulting non-local nonsymmetric system of ordinary differential equations (ODEs) is discretized by three iterative numerical schemes using different time stepping. Results of numerical experiments which compare the efficiency of the numerical schemes are discussed. Results from numerical tests with synthetic and real data are presented and discussed, as well.https://www.mdpi.com/2073-8994/15/12/2099forage bee lossesspatial differential difference equationfinal time constraintinverse problemODEs systemnon-local forward problem |
| spellingShingle | Atanas Z. Atanasov Miglena N. Koleva Lubin G. Vulkov Inverse Problem Numerical Analysis of Forager Bee Losses in Spatial Environment without Contamination Symmetry forage bee losses spatial differential difference equation final time constraint inverse problem ODEs system non-local forward problem |
| title | Inverse Problem Numerical Analysis of Forager Bee Losses in Spatial Environment without Contamination |
| title_full | Inverse Problem Numerical Analysis of Forager Bee Losses in Spatial Environment without Contamination |
| title_fullStr | Inverse Problem Numerical Analysis of Forager Bee Losses in Spatial Environment without Contamination |
| title_full_unstemmed | Inverse Problem Numerical Analysis of Forager Bee Losses in Spatial Environment without Contamination |
| title_short | Inverse Problem Numerical Analysis of Forager Bee Losses in Spatial Environment without Contamination |
| title_sort | inverse problem numerical analysis of forager bee losses in spatial environment without contamination |
| topic | forage bee losses spatial differential difference equation final time constraint inverse problem ODEs system non-local forward problem |
| url | https://www.mdpi.com/2073-8994/15/12/2099 |
| work_keys_str_mv | AT atanaszatanasov inverseproblemnumericalanalysisofforagerbeelossesinspatialenvironmentwithoutcontamination AT miglenankoleva inverseproblemnumericalanalysisofforagerbeelossesinspatialenvironmentwithoutcontamination AT lubingvulkov inverseproblemnumericalanalysisofforagerbeelossesinspatialenvironmentwithoutcontamination |