Effectiveness of MATLAB and Neural Networks for Solving Nonlinear Equations by Repetitive Methods

Abstract

Finding solutions to nonlinear equations is not only a matter for mathematicians but is essential in many branches such as physics, statistics, and others. However, some of the nonlinear equations in numerical analysis require a lot of complex calculations to achieve convergence. This leads to many arithmetic errors and is consumed a great effort to solve them. Hence, researchers in numerical analysis use computer programs to find approximate solutions. This study used Matlab and Artificial Neural Networks and applied two different numerical analysis methods. The results from training artificial neural networks by utilizing the Backpropagation algorithm and MATLAB have been compared. The importance of this study lies in shedding light on the capabilities of Matlab and its strength in the field of methods for solving mathematical series, and helps students in mathematics in solving complex equations faster and more accurately, also studying the utilization of Artificial Neural Network algorithms in solving these methods, and clarifying the difference between them and programming Ordinary Matlab and comparing them with ordinary mathematical methods. The findings revealed that Traditional methods need more effort. MATLAB helps. On the other hand, solving numerical analysis problems is easier, faster, more accurate, and more effective. Furthermore, in the case of the Matlab application, the Newton method gave faster and less in the number of steps. Additionally, in training, the neural network based on the Newton method gave results faster depending on the Bisection method.