Gudermannian Neural Networks for Two-Point Nonlinear Singular Model Arising in the Thermal-Explosion Theory
The goal of this research is to design the Gudermannian neural networks (GNNs) to solve a type of two-point nonlinear singular boundary value problems (TPN-SBVPs) that arise within thermal-explosion theory. The results of these investigation are provided for different neurons (4, 12 and 20), as well...
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| Published in | Neural processing letters Vol. 56; no. 4; p. 206 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
26.06.2024
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1573-773X 1370-4621 1573-773X |
| DOI | 10.1007/s11063-024-11512-4 |
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| Abstract | The goal of this research is to design the Gudermannian neural networks (GNNs) to solve a type of two-point nonlinear singular boundary value problems (TPN-SBVPs) that arise within thermal-explosion theory. The results of these investigation are provided for different neurons (4, 12 and 20), as well as absolute error along with the time complexity. For solving the TPN-SBVPs, a genetic algorithm (GA) and sequential quadratic programming (SQP) are used to optimize the error function. The accuracy of designed GNNs is provided by using a hybrid GA–SQP combination, which is based on a comparison of obtained and actual solutions. Furthermore, statistical analysis of the data is proposed in order to establish the competence as well as effectiveness of designed and the efficacy of the designed computing framework for solving the TPN-SBVPs. |
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| AbstractList | The goal of this research is to design the Gudermannian neural networks (GNNs) to solve a type of two-point nonlinear singular boundary value problems (TPN-SBVPs) that arise within thermal-explosion theory. The results of these investigation are provided for different neurons (4, 12 and 20), as well as absolute error along with the time complexity. For solving the TPN-SBVPs, a genetic algorithm (GA) and sequential quadratic programming (SQP) are used to optimize the error function. The accuracy of designed GNNs is provided by using a hybrid GA–SQP combination, which is based on a comparison of obtained and actual solutions. Furthermore, statistical analysis of the data is proposed in order to establish the competence as well as effectiveness of designed and the efficacy of the designed computing framework for solving the TPN-SBVPs. |
| ArticleNumber | 206 |
| Author | Fatima, Samara Sabir, Zulqurnain Baleanu, Dumitru Alhazmi, Sharifah E. |
| Author_xml | – sequence: 1 givenname: Samara surname: Fatima fullname: Fatima, Samara email: fatimasamara624@gmail.com organization: Department of Applied Mathematics, School of Mathematics and Statistics, Xi’an Jiaotong University – sequence: 2 givenname: Zulqurnain surname: Sabir fullname: Sabir, Zulqurnain organization: Department of Computer Science and Mathematics, Lebanese American University – sequence: 3 givenname: Dumitru surname: Baleanu fullname: Baleanu, Dumitru organization: Department of Computer Science and Mathematics, Lebanese American University – sequence: 4 givenname: Sharifah E. surname: Alhazmi fullname: Alhazmi, Sharifah E. organization: Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University |
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| Keywords | Singular Nonlinear Two-points Genetic algorithm Thermal explosion Complexity |
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| SubjectTerms | Approximation Artificial Intelligence Boundary value problems Complex Systems Computational Intelligence Computer Science Error functions Explosions Genetic algorithms Methods Neural networks Neurons Optimization techniques Quadratic programming Statistical analysis |
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| Title | Gudermannian Neural Networks for Two-Point Nonlinear Singular Model Arising in the Thermal-Explosion Theory |
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