Eventos Anais de eventos
CREEM2024
CREEM 2024 - XXX Congresso Nacional de Estudantes de Engenharia Mecânica
MÉTODO DAS DIFERENÇAS FINITAS PARA SOLUÇÃO DE EQUAÇÕES DIFERENCIAIS PARCIAIS APLICADAS À ENGENHARIA MECÂNICA
Submission Author:
Luís Otávio Alvarenga , MG , Brazil
Co-Authors:
Luís Otávio Alvarenga , Nelson Inforzato
Presenter: Luís Otávio Alvarenga
doi://10.26678/ABCM.CREEM2024.CRE2024-0067
Abstract
This work presents a theoretical and practical approach to numerical methods applied to the solution of partial differential equations (PDEs). Initially, a review of Taylor series and its implementation in numerical differentiation is conducted, highlighting the Finite Difference Method as a technique to approximate derivatives, in this case, first and second order. Subsequently, the solution of second-order PDEs such as Laplace's equation, the one-dimensional wave equation, and the diffusion equation is explored through the Finite Difference Method. Practical examples are analyzed, including the determination of temperature distribution in square plates under steady-state conditions and the temporal evolution of temperature in transient regimes. The study emphasizes the relevance and applicability of numerical methods in solving engineering and physics problems.
Keywords
numerical, Diffusion, Laplace, Derivatives, engineering
