Solving of the damped wave equation

Project members: 1

This project was aimed to solve the damped wave equation and analyse it in Matlab. The solution should be made with a damping coefficient that was decided with according to a previously known algorithm involving ones personal ID number.

I started out with the damped wave equation and moved on to a discretisation of the problem:

By setting in the damping coefficient and using the chain rule the equation can be expressed as:

 

Discretisation (using central difference) and the Method of Lines I got the following expression:

Then the vector f was further expressed using the boundary conditions applied.

The continues case was then solved using Matlab and different amount of discretion points. Some results can be seen in the images but more details, images and Matlab code is to be found below:

Full report (Swedish)