Integració numèrica d'EDOs

Abstract

[en] The goal of this work is to study several methods for solving initial value problems in ordinary differential equations (ODEs). Particularly, we focus on the most common one-step methods, Euler, Heun and Runge-Kutta. In addition, we will prove some classic theorems about the convergence of general one-step methods and their order of error. After that, we apply numerical integration to analyse a case study which proposes a socio-economic model of the interaction among three social classes to predict the raises and falls of civilisations.