El m\`etode de les l\'inies per a la resoluci\'o num\`erica d'equacions en derivades parcials. The method of lines for numerical solutions of partial differential equations

In this paper, we describe a semi-discrete method for a numerical resolution of a type of partial differential equations, called the method of lines (MOL). This method is based on the discretization of all but one of the variables of the problem. We illustrate this method by solving the Laplace equation in Cartesian coordinates. We compare the concepts used by the MOL with respect to the analytical method of variable separation. We show that the results obtained with the MOL are very good approximations of the analytical solutions.