An effective wavelet neural network approach for solving first and second order ordinary differential equations
The development of efficient numerical methods for obtaining numerical solutions of first and second order ordinary differential equations (ODEs) is of paramount importance, given the widespread utilization of ODEs as a means of characterizing the behavior in various scientific and engineering dis...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024
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| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/10955/1/J17457_9251095dacb9d8749bd891bfd7c49760.pdf |
| _version_ | 1825638447646244864 |
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| author | Lee Sen Tan, Lee Sen Tan Zainuddin, Zarita Pauline Ong, Pauline Ong Abdullah, Farah Aini A |
| author_facet | Lee Sen Tan, Lee Sen Tan Zainuddin, Zarita Pauline Ong, Pauline Ong Abdullah, Farah Aini A |
| author_sort | Lee Sen Tan, Lee Sen Tan |
| collection | UTHM |
| description | The development of efficient numerical methods for obtaining numerical solutions of first and second order
ordinary differential equations (ODEs) is of paramount importance, given the widespread utilization of ODEs as a
means of characterizing the behavior in various scientific and engineering disciplines. While various artificial neural networks (ANNs) approaches have recently emerged as potential solutions for approximating ODEs, the limited accuracy of existing models necessitates further advancements. Hence, this study presents a stochastic
model utilizing wavelet neural networks (WNNs) to approximate ODEs. Leveraging the compact structure and
fast learning speed of WNNs, an improved butterfly optimization algorithm (IBOA) is employed to optimize the
adjustable weights, facilitating more effective convergence towards the global optimum. The proposed WNNs approach is then rigorously evaluated by solving first and second order ODEs, including initial value problems, singularly perturbed boundary value problems, and a Lane–Emden type equation. Comparative analyses against alternative training methods, other existing ANNs, and numerical techniques demonstrate the superior performance of the proposed method, affirming its efficiency and accuracy in approximating ODE solutions. |
| first_indexed | 2024-09-24T00:08:58Z |
| format | Article |
| id | uthm.eprints-10955 |
| institution | Universiti Tun Hussein Onn Malaysia |
| language | English |
| last_indexed | 2024-09-24T00:08:58Z |
| publishDate | 2024 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | uthm.eprints-109552024-05-13T11:52:43Z http://eprints.uthm.edu.my/10955/ An effective wavelet neural network approach for solving first and second order ordinary differential equations Lee Sen Tan, Lee Sen Tan Zainuddin, Zarita Pauline Ong, Pauline Ong Abdullah, Farah Aini A T Technology (General) The development of efficient numerical methods for obtaining numerical solutions of first and second order ordinary differential equations (ODEs) is of paramount importance, given the widespread utilization of ODEs as a means of characterizing the behavior in various scientific and engineering disciplines. While various artificial neural networks (ANNs) approaches have recently emerged as potential solutions for approximating ODEs, the limited accuracy of existing models necessitates further advancements. Hence, this study presents a stochastic model utilizing wavelet neural networks (WNNs) to approximate ODEs. Leveraging the compact structure and fast learning speed of WNNs, an improved butterfly optimization algorithm (IBOA) is employed to optimize the adjustable weights, facilitating more effective convergence towards the global optimum. The proposed WNNs approach is then rigorously evaluated by solving first and second order ODEs, including initial value problems, singularly perturbed boundary value problems, and a Lane–Emden type equation. Comparative analyses against alternative training methods, other existing ANNs, and numerical techniques demonstrate the superior performance of the proposed method, affirming its efficiency and accuracy in approximating ODE solutions. Elsevier 2024 Article PeerReviewed text en http://eprints.uthm.edu.my/10955/1/J17457_9251095dacb9d8749bd891bfd7c49760.pdf Lee Sen Tan, Lee Sen Tan and Zainuddin, Zarita and Pauline Ong, Pauline Ong and Abdullah, Farah Aini A (2024) An effective wavelet neural network approach for solving first and second order ordinary differential equations. Applied Soft Computing, 154. pp. 1-17. https://doi.org/10.1016/j.asoc.2024.111328 |
| spellingShingle | T Technology (General) Lee Sen Tan, Lee Sen Tan Zainuddin, Zarita Pauline Ong, Pauline Ong Abdullah, Farah Aini A An effective wavelet neural network approach for solving first and second order ordinary differential equations |
| title | An effective wavelet neural network approach for solving first and second order ordinary differential equations |
| title_full | An effective wavelet neural network approach for solving first and second order ordinary differential equations |
| title_fullStr | An effective wavelet neural network approach for solving first and second order ordinary differential equations |
| title_full_unstemmed | An effective wavelet neural network approach for solving first and second order ordinary differential equations |
| title_short | An effective wavelet neural network approach for solving first and second order ordinary differential equations |
| title_sort | effective wavelet neural network approach for solving first and second order ordinary differential equations |
| topic | T Technology (General) |
| url | http://eprints.uthm.edu.my/10955/1/J17457_9251095dacb9d8749bd891bfd7c49760.pdf |
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