Modelización de la ecuación de calor con diferencias finitas

Abstract

[en] The aim of this paper is to demonstrate how to use what is learned as a graduate to intuitively resolve a problem and expand the knowledge on it. In this case the heat equation is resolved using some of the numerical methods studied along with a collection of other methods not presented during the math career. The way is solved, using finite differences method means that solving a partial differential equation resumes in using Taylor, resolving an ordinary differential equation and finding the solution of a big dimension sparse linear system. With this process the aim of this project will be satisfied and an approximation of the real temperature for each point in space and time will be found. In order to wite this paper a software was developed where three different ways of resolving differential equations and four different methods to resolve the linear system. This software will output the aproximation using all combinations with the number of iterations, time of execution and the error with the real solution. All together, the reader should have a good understaing of how Finite Difference Method works, some ways to approximate the temperature described with the Dirichlet condition in a given domain and will end up with a first modelling experience.