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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/189887
Equacions diferencials ordinàries i diferenciació automàtica
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[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.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Àngel Jorba i Monte
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GUBAU GUBERT, Clara. Equacions diferencials ordinàries i diferenciació automàtica. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/189887