Introdução aos métodos analíticos e numéricos para equações diferenciais parciais: uma aplicação à equação do telégrafo

Abstract

At the end of the 19th century, Oliver Heaviside began research on transmission of information, developing the Telegraph equation, which describes the propagation of waves and currents in cables. Since then, this partial differential equation (PDE) has been extensively studied. The objectives of this work were to present an introduction to the fundamental concepts of PDEs and their numerical solutions using the finite difference method. A dedicated chapter focuses on the Telegraph equation, including numerical simulations to illustrate the application. Additionally, the work seeks to serve as a reference material for teachers and students, contributing to the teaching of PDEs through a structured teaching sequence and the provision of codes used in the numerical implementations.