Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/181641
Title: El problema de Stefan
Author: Ramos Llauradó, Sara
Director/Tutor: Bosch Gual, Miquel
Keywords: Problemes de contorn
Treballs de fi de grau
Equacions en derivades parcials
Anàlisi numèrica
Transmissió de la calor
Boundary value problems
Bachelor's theses
Partial differential equations
Numerical analysis
Transmission of heat
Issue Date: 23-Jan-2021
Abstract: [en] In this tesis we study the one-dimensional Stefan problem, a classic example of a free boundary value problem for a partial differential equation. We will look at the Stefan condition and some techniques applied to problem solving. Furthermore, we will discuss the existence and uniqueness of heat equation, as well as the maximum principle. Finally the problem is solved numerically using the Crank-Nicolson scheme, for two different boundary conditions: one constant and the other time-dependent; doing an asymptotic analysis at the initial time, and an analysis of the approximation errors. The approximate solutions are shown graphically along with proper error estimates.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Miquel Bosch Gual
URI: http://hdl.handle.net/2445/181641
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques
Programari - Treballs de l'alumnat

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