Bibliographic citations
Torres, S., (2020). Implementación numérica de una ecuación diferencial de movimiento en un grado de libertad con componente estocástica [Tesis, Pontificia Universidad Católica del Perú]. http://hdl.handle.net/20.500.12404/17212
Torres, S., Implementación numérica de una ecuación diferencial de movimiento en un grado de libertad con componente estocástica [Tesis]. PE: Pontificia Universidad Católica del Perú; 2020. http://hdl.handle.net/20.500.12404/17212
@mastersthesis{renati/16703,
title = "Implementación numérica de una ecuación diferencial de movimiento en un grado de libertad con componente estocástica",
author = "Torres Murga, Saul Moises",
publisher = "Pontificia Universidad Católica del Perú",
year = "2020"
}
In dynamics, using the ordinary differential equation of motion, it is possible to determine the position in time of a moving mass because it is disturbed by some deterministic action. In this work it was proposed to apply to the mass a non-deterministic disturbance of seismic origin in a vertical degree of freedom and within the linear range. The research question was: Will it be possible to migrate the ordinary differential equation (ODE) of motion to a stochastic differential equation (SDE) of motion? Under this framework, the foundations of probability theory and stochastic processes were studied. Using these branches of applied mathematics, an SDE of movement was obtained. The Euler-Maruyama approximation was also studied, which was implemented, after verifying its stochastic and numerical stability, to obtain a solution of the EDE of the movement found. The results obtained confirmed that the use of a non-deterministic version generates satisfactory results. It is recommended to carry out similar analyzes with other variables, for instance, in systems with a different degree of freedom, with more than one degree of freedom and / or considering non-linear behavior.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.