An effective wavelet neural network approach for solving first and second order ordinary differential equations

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.

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Abstract

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.

Item Type:	Article
Uncontrolled Keywords:	Wavelet neural networks Improved butterfly optimization algorithm Ordinary differential equations, Initial value problems, Boundary value problems
Subjects:	T Technology > T Technology (General)
Divisions:	Faculty of Mechanical and Manufacturing Engineering
Depositing User:	Mr. Mohamad Zulkhibri Rahmad
Date Deposited:	13 May 2024 11:52
Last Modified:	13 May 2024 11:52
URI:	http://eprints.uthm.edu.my/id/eprint/10955

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