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Title: Mètodes numèrics per a equacions diferencials ordinàries
Author: Castell Fàbregues, Jaume
Director/Tutor: Jorba i Monte, Àngel
Keywords: Equacions diferencials ordinàries
Treballs de fi de grau
Anàlisi numèrica
Problemes de valor inicial
Ordinary differential equations
Bachelor's thesis
Numerical analysis
Initial value problems
Issue Date: 27-Jun-2016
Abstract: Mainly, the project studies some methods for numerical integration to approximate the solutions of ordinary differential equations, from now on they will be called ODE’s. Firstly, some concepts based on numerical methods for initial value problems studied during the degree subject Mètodes Numèrics 2 are reviewed and extended. We studied the Taylor methods, using automatic differentiation to compute the set of derivatives of a function, the Runge-Kutta methods and, as a variant of these, the Runge-Kutta-Fehlberg methods that lets us to control the step size. The next section of the project consists in the study of the stability of periodic orbits (Floquet’s theorem) and orbit’s continuation regarding to parameters. Finally, the last part studies a couple examples of classical mechanics where the tools learned on the first part of the project are used: pendulum periodically disturbed and Bicircular model. In both cases we explain the process to compute the periodic orbits and it’s stability. In this process, we use some concepts studied in Equacions Diferencials subject: variational equations and Poincaré map.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Àngel Jorba i Monte
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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