Fractional Partial Differential Equation Modeling for Solar Cell Charge Dynamics
This paper presents a groundbreaking numerical approach, the fractional differential quadrature method (FDQM), to simulate the complex dynamics of organic polymer solar cells. The method, which leverages polynomial-based differential quadrature and Cardinal sine functions coupled with the Caputo-typ...
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MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/12/729 |
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| author | Waleed Mohammed Abdelfattah Ola Ragb Mohamed Salah Mohamed S. Matbuly Mokhtar Mohamed |
| author_facet | Waleed Mohammed Abdelfattah Ola Ragb Mohamed Salah Mohamed S. Matbuly Mokhtar Mohamed |
| author_sort | Waleed Mohammed Abdelfattah |
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| description | This paper presents a groundbreaking numerical approach, the fractional differential quadrature method (FDQM), to simulate the complex dynamics of organic polymer solar cells. The method, which leverages polynomial-based differential quadrature and Cardinal sine functions coupled with the Caputo-type fractional derivative, offers a significant improvement in accuracy and efficiency over traditional methods. By employing a block-marching technique, we effectively address the time-dependent nature of the governing equations. The efficacy of the proposed method is validated through rigorous numerical simulations and comparisons with existing analytical and numerical solutions. Each scheme’s computational characteristics are tailored to achieve high accuracy, ensuring an error margin on the order of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>8</mn></mrow></msup><mo> </mo></mrow></semantics></math></inline-formula> or less. Additionally, a comprehensive parametric study is conducted to investigate the impact of key parameters on device performance. These parameters include supporting conditions, time evolution, carrier mobilities, charge carrier densities, geminate pair distances, recombination rate constants, and generation efficiency. The findings of this research offer valuable insights for optimizing and enhancing the performance of organic polymer solar cell devices. |
| format | Article |
| id | doaj-art-422490a4ec41436f836c3e43a9b6e91a |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
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| series | Fractal and Fractional |
| spelling | doaj-art-422490a4ec41436f836c3e43a9b6e91a2024-12-27T14:27:08ZengMDPI AGFractal and Fractional2504-31102024-12-0181272910.3390/fractalfract8120729Fractional Partial Differential Equation Modeling for Solar Cell Charge DynamicsWaleed Mohammed Abdelfattah0Ola Ragb1Mohamed Salah2Mohamed S. Matbuly3Mokhtar Mohamed4College of Engineering, University of Business and Technology, Jeddah 23435, Saudi ArabiaDepartment of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, Zagazig P.O. Box 44519, EgyptDepartment of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, Zagazig P.O. Box 44519, EgyptDepartment of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, Zagazig P.O. Box 44519, EgyptBasic Science Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa 11152, EgyptThis paper presents a groundbreaking numerical approach, the fractional differential quadrature method (FDQM), to simulate the complex dynamics of organic polymer solar cells. The method, which leverages polynomial-based differential quadrature and Cardinal sine functions coupled with the Caputo-type fractional derivative, offers a significant improvement in accuracy and efficiency over traditional methods. By employing a block-marching technique, we effectively address the time-dependent nature of the governing equations. The efficacy of the proposed method is validated through rigorous numerical simulations and comparisons with existing analytical and numerical solutions. Each scheme’s computational characteristics are tailored to achieve high accuracy, ensuring an error margin on the order of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>8</mn></mrow></msup><mo> </mo></mrow></semantics></math></inline-formula> or less. Additionally, a comprehensive parametric study is conducted to investigate the impact of key parameters on device performance. These parameters include supporting conditions, time evolution, carrier mobilities, charge carrier densities, geminate pair distances, recombination rate constants, and generation efficiency. The findings of this research offer valuable insights for optimizing and enhancing the performance of organic polymer solar cell devices.https://www.mdpi.com/2504-3110/8/12/729fractional derivativeblock marchingdifferential quadraturerenewable energyorganic solar cellsCaputo |
| spellingShingle | Waleed Mohammed Abdelfattah Ola Ragb Mohamed Salah Mohamed S. Matbuly Mokhtar Mohamed Fractional Partial Differential Equation Modeling for Solar Cell Charge Dynamics Fractal and Fractional fractional derivative block marching differential quadrature renewable energy organic solar cells Caputo |
| title | Fractional Partial Differential Equation Modeling for Solar Cell Charge Dynamics |
| title_full | Fractional Partial Differential Equation Modeling for Solar Cell Charge Dynamics |
| title_fullStr | Fractional Partial Differential Equation Modeling for Solar Cell Charge Dynamics |
| title_full_unstemmed | Fractional Partial Differential Equation Modeling for Solar Cell Charge Dynamics |
| title_short | Fractional Partial Differential Equation Modeling for Solar Cell Charge Dynamics |
| title_sort | fractional partial differential equation modeling for solar cell charge dynamics |
| topic | fractional derivative block marching differential quadrature renewable energy organic solar cells Caputo |
| url | https://www.mdpi.com/2504-3110/8/12/729 |
| work_keys_str_mv | AT waleedmohammedabdelfattah fractionalpartialdifferentialequationmodelingforsolarcellchargedynamics AT olaragb fractionalpartialdifferentialequationmodelingforsolarcellchargedynamics AT mohamedsalah fractionalpartialdifferentialequationmodelingforsolarcellchargedynamics AT mohamedsmatbuly fractionalpartialdifferentialequationmodelingforsolarcellchargedynamics AT mokhtarmohamed fractionalpartialdifferentialequationmodelingforsolarcellchargedynamics |