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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: | Programari - Treballs de l'alumnat Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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codi_font.zip | Codi font | 19.12 kB | zip | View/Open |
tfg_sara_ramos_llaurado.pdf | Memòria | 848.43 kB | Adobe PDF | View/Open |
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