Aplicação dos métodos Shooting e diferenças finitas na obtenção da curva elástica em uma viga

Abstract

In this study, the numerical solution for the Boundary Value Problem (BVP) describing the elastic curve of a simply supported and uniformly loaded beam was developed using the Finite Difference Method (FDM) and the Shooting Method. The analytical solution was also obtained in order to verify the proximity between the numerical and analytical solutions of the BVP. The research was based on theoretical references on Ordinary Differential Equations and Numerical Calculus, aiming to achieve efficiency and accuracy in the numerical solutions obtained incomparison with the analytical solution. The methods were implemented using the Python programming language, which made it possible to perform the calculations and generate graphical representations of the solutions. The results showed that the numerical solutions agreed with the analytical solution, demonstrating the accuracy of the applied methods. Thus, the study confirms the importance of numerical methods in solving differential equations, especially in cases where the analytical solution is difficult to construct or cannot be obtained, establishing numerical methods as an essential tool for solving problems in mathematics and engineering.