Numerical and Analytical Analysis of Separation of Variables and Finite Difference Methods in the Modeling of Partial Differential Equations

Abstract

In this project we will study methods for solving Partial Differential Equations (PDE). Begin by conducting a theoretical analysis of these equations, boundary problems and means for their solution. We will carry out by analytical method of separation of variables to be applied in the classical equations of heat, wave and Laplace. The intention is to model a Boundary Value Problem (BVP) for subsequent formulation and implementation of the Finite Difference Method (FDM). At this stage, we are interested in conducting a case study focusing on physical applications. Thus, we will seek to emphasize the search for the meaning of content with the consequences of the theoretical results, while we support you in a computational tool for calculation cumbersome and some graphical views necessary to the theme. We understand that the project will explore the mathematical content in many ways - algebraic, analytic, numeric, geometric, visual - looking to extend the maximum capability of understanding the concepts and possible interrelationships. In this way, we aim to provide the student gain experience both in the theoretical part of the issue as the numerical application in known physical problems