Resolução de análise nodal com auxílio de métodos numéricos

Abstract

Usually for the knowledge of the voltages in the electrical circuits it is used the nodal analysis. The nodal analysis is based on Kirchoff’s Law of Currents and Ohm’s Law, where we determine the potential difference between nodes in an electric circuit. Each node produces an equation, thus forming a system of equations that can be solved by numerical methods. This work aims to perform the nodal analysis of a base circuit using the numerical methods Gauss Elimination, LU Factoration, QR Factoration and Crout Method for the solution of linear systems. All numerical methods were implemented in C programming language and the analysis of the accuracy of the results was given by the relative error in comparison to the results obtained by MatLab software. For this process, a base circuit was used that in its nodal analysis generated a linear system of seven equations and seven unknowns. After the conclusion, it was possible to assume that the development of the work provided the application and programming of numerical methods for solution of linear systems in Problems of Electrical Engineering, presenting solutions as exact as those obtained by commercial mathematical software.