Numerical simulation of fractional power diffusion biosensors
The main aim of this paper is to propose new mathematical models for simulation of biosensors and to construct and investigate discrete methods for the efficient solution of the obtained systems of nonlinear PDEs. The classical linear diffusion operators are substituted with nonlocal fractional pow...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2023-03-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://limes.vgtu.lt/index.php/MMA/article/view/17583 |
| _version_ | 1797866219056922624 |
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| author | Ignas Dapšys Raimondas Čiegis |
| author_facet | Ignas Dapšys Raimondas Čiegis |
| author_sort | Ignas Dapšys |
| collection | DOAJ |
| description |
The main aim of this paper is to propose new mathematical models for simulation of biosensors and to construct and investigate discrete methods for the efficient solution of the obtained systems of nonlinear PDEs. The classical linear diffusion operators are substituted with nonlocal fractional powers of elliptic operators. The splitting type finite volume scheme is used as a basic template for the introduction of new mathematical models. Therefore the accuracy of the splitting scheme is investigated and compared with the symmetric Crank-Nicolson scheme. The dependence of the approximation error on the regularity of the solution is investigated. Results of computational experiments for different values of fractional parameters are presented and analysed.
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| first_indexed | 2024-04-09T23:21:34Z |
| format | Article |
| id | doaj.art-36df2df7944143148b240c3e11103bb8 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-04-09T23:21:34Z |
| publishDate | 2023-03-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-36df2df7944143148b240c3e11103bb82023-03-21T16:16:51ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102023-03-0128210.3846/mma.2023.17583Numerical simulation of fractional power diffusion biosensorsIgnas Dapšys0Raimondas Čiegis1Department of Mathematical Modeling, Vilnius Gediminas Technical University, Saulėtekio al. 11, Vilnius, LithuaniaDepartment of Mathematical Modeling, Vilnius Gediminas Technical University, Saulėtekio al. 11, Vilnius, Lithuania The main aim of this paper is to propose new mathematical models for simulation of biosensors and to construct and investigate discrete methods for the efficient solution of the obtained systems of nonlinear PDEs. The classical linear diffusion operators are substituted with nonlocal fractional powers of elliptic operators. The splitting type finite volume scheme is used as a basic template for the introduction of new mathematical models. Therefore the accuracy of the splitting scheme is investigated and compared with the symmetric Crank-Nicolson scheme. The dependence of the approximation error on the regularity of the solution is investigated. Results of computational experiments for different values of fractional parameters are presented and analysed. https://limes.vgtu.lt/index.php/MMA/article/view/17583mathematical modellingdiffusion-reaction equationsfractional power of elliptic operatorsfinite volume schemessplitting methodbiosensors |
| spellingShingle | Ignas Dapšys Raimondas Čiegis Numerical simulation of fractional power diffusion biosensors Mathematical Modelling and Analysis mathematical modelling diffusion-reaction equations fractional power of elliptic operators finite volume schemes splitting method biosensors |
| title | Numerical simulation of fractional power diffusion biosensors |
| title_full | Numerical simulation of fractional power diffusion biosensors |
| title_fullStr | Numerical simulation of fractional power diffusion biosensors |
| title_full_unstemmed | Numerical simulation of fractional power diffusion biosensors |
| title_short | Numerical simulation of fractional power diffusion biosensors |
| title_sort | numerical simulation of fractional power diffusion biosensors |
| topic | mathematical modelling diffusion-reaction equations fractional power of elliptic operators finite volume schemes splitting method biosensors |
| url | https://limes.vgtu.lt/index.php/MMA/article/view/17583 |
| work_keys_str_mv | AT ignasdapsys numericalsimulationoffractionalpowerdiffusionbiosensors AT raimondasciegis numericalsimulationoffractionalpowerdiffusionbiosensors |