Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/189887
Title: | Equacions diferencials ordinàries i diferenciació automàtica |
Author: | Gubau Gubert, Clara |
Director/Tutor: | Jorba i Monte, Àngel |
Keywords: | Equacions diferencials ordinàries Treballs de fi de grau Anàlisi numèrica Fórmules de Runge-Kutta Ordinary differential equations Bachelor's theses Numerical analysis Runge-Kutta formulas |
Issue Date: | 13-Jun-2022 |
Abstract: | [en] Automatic differentiation is an alternative method to compute the derivatives of a function in a given point. This method requires that the function can be written as a sequence of elementary operations and basic functions like exponential or trigonometry ones. Once we have our function as a combination of those elements, we can compute it and find its derivatives. Moreover, there are the Poincaré sections. This is a really common tool used to study dynamical systems, but the computation of its derivatives used to be a frequent computational problem. In order to solve this, we can use automatic differentiation. More precisely, we will study how to modify a numerical integrator to compute automatically the derivatives of the flow of a differential equation regarding some initial conditions. The numerical integrator that we will use is Runge-Kutta-Fehlberg of order 4 and 5. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Àngel Jorba i Monte |
URI: | http://hdl.handle.net/2445/189887 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
tfg_gubau_gubert_clara.pdf | Memòria | 1 MB | Adobe PDF | View/Open |
This item is licensed under a
Creative Commons License