Bosch Gual, MiquelRamos Llauradó, Sara2021-12-032021-12-032021-01-23https://hdl.handle.net/2445/181641Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Miquel Bosch Gual[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.69 p.application/pdfcatcc-by-nc-nd (c) Sara Ramos Llauradó, 2021http://creativecommons.org/licenses/by-nc-nd/3.0/es/Problemes de contornTreballs de fi de grauEquacions en derivades parcialsAnàlisi numèricaTransmissió de la calorBoundary value problemsBachelor's thesesPartial differential equationsNumerical analysisTransmission of heatinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess