Métodos numéricos em problemas físicos de valor inicial para equações diferenciais ordinárias

Abstract

This work presents some numerical methods used to solve problems belonging to a class of ordinary differential equations known as initial value problems. Although this is but an introductory text, it brings the bases for solving complex problems based on molecular dynamics simulations. The first chapter presents some physical situations which fall within the class of initial value problems, and the theoretical ground needed to solve them. The second chapter shows ways to describe, from the computational point of view, the problems discussed in the previous chapter, as well as some important concepts and numerical methods to solve these problems. In the last chapter, the problems presented in the first chapter are solved using the numerical methods described in the second chapter. Finally, we analyze convergence, accuracy, and techniques for evaluating the error observed in the methods discussed.