Programa de aplicação para resolver sistemas de equações não lineares

Abstract

Introduction: Application programs in mathematics have had a significant impact on solving nonlinear systems of equations and are impacting various areas. In a nonlinear equation, it is not always easy to determine its root or convergence point; one must analyze and restrict the behavior of the functions that comprise it. Objective: To develop a mathematical program to solve nonlinear systems of equations, selecting the most efficient method and presenting results that include the analysis of convergence and stability of the implemented iterative methods. Method: To solve the system of type V(X)=0, methods such as Simple Iteration, Gradient, Newton, Modified Newton, and Quasi-Newton were used. Visual C++ 6.0 programming language along with Matlab 6.5 libraries were used for the development of the application program for mathematical notations. Results: An application program named SMENLI (Mathematical Software for solving Nonlinear Equations) was developed, which implemented various iterative methods to solve 20 systems of nonlinear equations. Of these, 15 converged and 5 diverged. Some did not converge due to the initial point provided to the program, which utilizes a lexical analyzer. Additionally, it is important to remember that not all systems of nonlinear equations have a solution. Conclusions: It was found that the Newton and Modified Newton methods are the most efficient in terms of convergence, standing out for their shorter time and fewer iterations compared to other implemented methods. However, in exceptional cases with certain systems of nonlinear equations, the Quasi-Newton method may prove superior to others.