Developing a second order accurate level-set method for solving the one-dimensional Stefan problem

This work aims at finding a second order accurate level-set method which solves the Stefan problem with non-homogeneous Dirichlet boundary conditions in one dimension. The numerical accuracy of the FTCS-scheme, BTCS-scheme and Crank-Nicolson scheme for the discretization of the heat equation was considered, as well as the accuracy of the first...