Resolução de equações diferenciais ordinárias: problema de valor de contorno

Abstract

This work aimed to carry out a study on boundary value problems (PVC), applying analytical and numerical resolution techniques of the ordinary differential equations (EDO) that model the analyzed PVC’s and perform the comparison between the results obtained, with the numerical simulation being performed in Scilab software. The main analyzed PVC deals with the heat distribution in a heated metal rod positioned between two walls with constant, but distinct temperatures, the EDO that models the system is inhomogeneous second order linear and contains the system-specific heat transfer coefficient , which takes into account the convection and conduction transfers present in the system. The method of indeterminate coefficients was used to determine the analytical solution of PVC, while for numerical solution the finite difference method (MDF) was used, replacing the derivatives of the original EDO with finite difference formulas, thus obtaining a set of simultaneous algebraic equations, solved by the Gaussian Elimination method. The numerical results were compared with the analytical solution, obtaining a low relative error, which shows the efficiency of the numerical result.