A comparison between artificial intelligence techniques and traditional techniques in approximating solutions to differential equations

Abstract

The purpose of this study is to examine and compare the efficiency of conventional numerical methods versus AI methods on approximating the solutions of the differential equation. These specific numerical and AI methods to be tested on differential equation were Euler, Rung-Kota, finite difference, artificial neural network, physics based neural network, genetic algorithm and a hybrid proposed model. In order to fulfill these aims the study adopted a comparative analytical research approach by utilizing evaluation on its performance based on numerous indexes such as; accuracy, flexibility, stability, computing time, recall, and F1 metric. It was shown that AI methods are more efficient than conventional numerical methods at complex nonlinear system problems. Among all the tested methods the proposed hybrid model shows the best performance with regard to highest accuracy, strongest stability and lowest error rate among all other method tested models. It was shown that AI and hybrid model This method outperformed traditional numerical methods in reducing error by 7% to 19%, stability by 4% to 23%, and accuracy by 8% to 19% and stability by 14% to 30%. Ease of use was also improved by 12%. Based on these results, it can be concluded that while traditional numerical methods remain useful for solving simple problems in terms of ease of use, applicability, and reliability based on mathematical formulation, artificial intelligence methods will become an integral part of scientific and engineering practices in solving approximation problems in differential equations.