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

被引：0

作者：

Tan, Lee Sen ^{[1
]}

Zainuddin, Zarita ^{[1
]}

Ong, Pauline ^{[2
]}

Abdullah, Farah Aini ^{[1
]}

机构：

[1] School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

[2] Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, Batu Pahat, Johor, Parit Raja,86400, Malaysia

来源：

Applied Soft Computing | 2024年 / 154卷

关键词：

Behavioral research - Initial value problems - Numerical methods - Optimization - Ordinary differential equations - Stochastic models - Stochastic systems;

D O I：

暂无

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学科分类号：

摘要：

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. © 2024 Elsevier B.V.

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