Bosch Gual, MiquelPech Alberich, Antoni2022-07-122022-07-122022-01-24https://hdl.handle.net/2445/187621Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Miquel Bosch Gual[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.81 p.application/pdfcatcc-by-nc-nd (c) Antoni Pech Alberich, 2022http://creativecommons.org/licenses/by-nc-nd/3.0/es/Anàlisi numèricaTreballs de fi de grauEquacions diferencials ordinàriesProblemes de valor inicialNumerical analysisBachelor's thesesOrdinary differential equationsInitial value problemsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess