Utilizing the Artificial Neural Network Approach for the Resolution of First-Order Ordinary Differential Equations
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Date
2024-06-16
Journal Title
Journal ISSN
Volume Title
Publisher
Penteract Technology, Malaysia
Abstract
Ordinary Differential Equations (ODEs) play a crucial role in various scientific and
professional domains for modeling dynamic systems and their behaviors. While traditional
numerical methods are widely used for approximating ODE solutions, they often face
challenges with complex or nonlinear systems, leading to high computational costs. This
study aims to address these challenges by proposing an artificial neural network (ANN)-
based approach for solving first-order ODEs. Through the introduction of the ANN
technique and exploration of its practical applications, we conduct numerical experiments
on diverse first-order ODEs to evaluate the convergence rate and computational efficiency
of the ANN. Our results from comprehensive numerical tests demonstrate the efficacy of the
ANN-generated responses, confirming its reliability and potential for various applications in
solving first-order ODEs with improved efficiency and accuracy.
Description
This research focuses on using Artificial Neural Networks (ANNs) to solve first-order Ordinary Differential Equations (ODEs). Traditional numerical methods often struggle with complex or nonlinear equations, especially in terms of computational efficiency. To tackle this, the study explores how ANNs—known for their ability to approximate complex functions—can be applied as an alternative solution technique. The approach involves training an ANN to learn the solution to different types of first-order ODEs. Through a series of numerical experiments, the study evaluates how well the ANN performs in terms of accuracy, convergence, and computational speed. The findings show that ANNs can be a reliable and efficient method for solving first-order ODEs, with potential applications in various scientific and engineering problems.
Keywords
First-Oder ODE, Artificial Neural Network, Computational Efficiency, Numerical Technique, Convergence Analysis
Citation
10.Audu, K. J., Marshal, B., Mohammed, U. & Yahaya, Y. A. (2024). Artificial Neural Network Approach for the Resolution of First-Order Ordinary Differential Equations. Malaysian Journal of Science and Advanced Technology, 4(3) 210-216.