Resolução da equação de Laplace na distribuição de temperatura em uma placa plana

• Main Author: Junges, Luana Caroline
• Publication Date: 2024
• Format: Bachelor thesis
• Language: por
• Source: Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT))
• Download full: http://repositorio.utfpr.edu.br/jspui/handle/1/35836
• topic: Equações diferenciais parciais; Diferenças finitas; Python (Linguagem de programação de computador); Differential equations, Partial; Finite differences; Python (Computer program language); CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work, the Laplace Equation, an elliptic partial differential equation (PDE) that describes equilibrium situations, was addressed. The objective was to compare the proximity of the numerical solution to the analytical solution in order to verify the applicability of numerical methods. The analytical solution was obtained using the method of separation of variables. In contrast, to find the numerical solution, the finite difference method (FDM) was applied. Both solutions were implemented in the Python language, allowing for the analysis of the graphs and the calculation of the relative error between the analytical and numerical solutions. It was found that the numerical solution provides a good approximation of the analytical solution of PDEs.