Utilizing the Artificial Neural Network Approach for the Resolution of First-Order Ordinary Differential Equations

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.