# 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

## TL;DR

This paper introduces the method of lines (MOL), a semi-discrete numerical technique for solving partial differential equations, demonstrated through the Laplace equation, showing high accuracy compared to analytical solutions.

## Contribution

It presents a detailed description of the MOL for PDEs and compares its effectiveness with the classical variable separation method.

## Key findings

- MOL provides accurate approximations of analytical solutions.
- The method discretizes all but one variable, simplifying PDE solving.
- Results show MOL's effectiveness for Laplace equation in Cartesian coordinates.

## Abstract

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.