Hybrid neural network framework for efficient solutions of third-order differential equations
- سال انتشار: 1404
- محل انتشار: فصلنامه ریاضی و علوم محاسباتی، دوره: 6، شماره: 3
- کد COI اختصاصی: JR_JMCS-6-3_008
- زبان مقاله: انگلیسی
- تعداد مشاهده: 12
نویسندگان
School of Mathematical Sciences, University Sains Malaysia, ۱۱۸۰۰ USM, Penang, Malaysia.
School of Mathematical Sciences, Universiti Sains Malaysia, ۱۱۸۰۰ USM, Penang, Malaysia.
Department of Mathematical Sciences, Osun State University, Osogbo, Nigeria
چکیده
Over the years and across various scientific fields, artificial neural networks (ANN) have achieved remarkable success. Among these is deep feedforward neural networks (FFNNs) which notably enhanced the accuracy of numerous tasks. Despite their capabilities, their potential for solving complex higher-order equations has not been extensively explored. This study introduces an innovative method to improve the accuracy and efficiency of solving third-order differential equations (ODEs) by combining a hybrid block method with feedforward neural networks (FFNNs). In this approach, neural networks which are a subset of neural computing, are utilized to develop a new solution technique for approximating third-order ODEs, leveraging advanced mathematical tools and neural-like computation systems. The hybrid block method divides the problem into manageable segments, while the FFNNs iteratively learn and refine the solutions. This combination harnesses the computational efficiency of block methods and the adaptive learning capabilities of FFNNs to enhance solution accuracy. We provide a detailed methodology for implementing this hybrid approach and validate its effectiveness through numerical experiments and comparisons with existing methods. The results indicate substantial improvements in accuracy and computational efficiency, suggesting that the proposed method is a promising tool for solving complex third-order ODEs in various domains.کلیدواژه ها
Machine Learning Integration, Algorithm Optimization, Computational Efficiency, Hybrid Methods, Block methodاطلاعات بیشتر در مورد COI
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