Computational Intelligence of Numerical Dynamics of Nanofluidic Model
This study investigates the flow dynamics of a nanofluid by modeling a system of nonlinear ordinary differential equations (ODEs). The system is transformed into a real dataset and solved using artificial neural networks (ANNs) trained via the Levenberg–Marquardt backpropagation (neural networks wit...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2025-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/ddns/3107171 |
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| _version_ | 1849435129504595968 |
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| author | Tahir Nawaz Cheema Ali Raza Maysaa Elmahi Abd Elwahab Ayesha Shabbir Sharafat Ali Emad Fadhal |
| author_facet | Tahir Nawaz Cheema Ali Raza Maysaa Elmahi Abd Elwahab Ayesha Shabbir Sharafat Ali Emad Fadhal |
| author_sort | Tahir Nawaz Cheema |
| collection | DOAJ |
| description | This study investigates the flow dynamics of a nanofluid by modeling a system of nonlinear ordinary differential equations (ODEs). The system is transformed into a real dataset and solved using artificial neural networks (ANNs) trained via the Levenberg–Marquardt backpropagation (neural networks with backpropagation and machine learning [NN-BPML]) method, incorporating the explicit Runge–Kutta (ERK) numerical approach. The ANNs are trained to approximate the solutions of the nonlinear system, with particular attention given to the physical relevance of parameters, notably the “⅄” governing nanofluid movement. A comprehensive analysis involving training, testing, validation, performance evaluation, and regression analysis is conducted. Numerical experiments explore both rapid and slow steady-state behaviors, revealing characteristics rarely observed in the integer-order models. The accuracy and stability of the proposed model are assessed through mean-squared error, error histograms, and regression plots, confirming the reliability of the developed computational framework. |
| format | Article |
| id | doaj-art-9c6ea021fd984d5589de2967d4e3a166 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-9c6ea021fd984d5589de2967d4e3a1662025-08-20T03:26:25ZengWileyDiscrete Dynamics in Nature and Society1607-887X2025-01-01202510.1155/ddns/3107171Computational Intelligence of Numerical Dynamics of Nanofluidic ModelTahir Nawaz Cheema0Ali Raza1Maysaa Elmahi Abd Elwahab2Ayesha Shabbir3Sharafat Ali4Emad Fadhal5Department of MathematicsDepartment of Physical SciencesDepartment of Mathematical SciencesDepartment of Physical SciencesDepartment of MathematicsDepartment of Mathematics & StatisticsThis study investigates the flow dynamics of a nanofluid by modeling a system of nonlinear ordinary differential equations (ODEs). The system is transformed into a real dataset and solved using artificial neural networks (ANNs) trained via the Levenberg–Marquardt backpropagation (neural networks with backpropagation and machine learning [NN-BPML]) method, incorporating the explicit Runge–Kutta (ERK) numerical approach. The ANNs are trained to approximate the solutions of the nonlinear system, with particular attention given to the physical relevance of parameters, notably the “⅄” governing nanofluid movement. A comprehensive analysis involving training, testing, validation, performance evaluation, and regression analysis is conducted. Numerical experiments explore both rapid and slow steady-state behaviors, revealing characteristics rarely observed in the integer-order models. The accuracy and stability of the proposed model are assessed through mean-squared error, error histograms, and regression plots, confirming the reliability of the developed computational framework.http://dx.doi.org/10.1155/ddns/3107171 |
| spellingShingle | Tahir Nawaz Cheema Ali Raza Maysaa Elmahi Abd Elwahab Ayesha Shabbir Sharafat Ali Emad Fadhal Computational Intelligence of Numerical Dynamics of Nanofluidic Model Discrete Dynamics in Nature and Society |
| title | Computational Intelligence of Numerical Dynamics of Nanofluidic Model |
| title_full | Computational Intelligence of Numerical Dynamics of Nanofluidic Model |
| title_fullStr | Computational Intelligence of Numerical Dynamics of Nanofluidic Model |
| title_full_unstemmed | Computational Intelligence of Numerical Dynamics of Nanofluidic Model |
| title_short | Computational Intelligence of Numerical Dynamics of Nanofluidic Model |
| title_sort | computational intelligence of numerical dynamics of nanofluidic model |
| url | http://dx.doi.org/10.1155/ddns/3107171 |
| work_keys_str_mv | AT tahirnawazcheema computationalintelligenceofnumericaldynamicsofnanofluidicmodel AT aliraza computationalintelligenceofnumericaldynamicsofnanofluidicmodel AT maysaaelmahiabdelwahab computationalintelligenceofnumericaldynamicsofnanofluidicmodel AT ayeshashabbir computationalintelligenceofnumericaldynamicsofnanofluidicmodel AT sharafatali computationalintelligenceofnumericaldynamicsofnanofluidicmodel AT emadfadhal computationalintelligenceofnumericaldynamicsofnanofluidicmodel |