How can I solve this (Euler–Bernoulli beam) ?

A simple model of the beam subjected to bending stresses is given by Euler-Bernoulli differential equation. Finite element discretization leads to a system of liniar equations.As discretization size decreases the system becomes larger and more ill-conditioned. For a beam fixed at both ends is obtained a system band width band size 5:

The right hand side of the system is the beam - applied forces. Choose it so that to have a known solution such as a deflection in the middle of the beam. Using an iterative method solve the system repeatedly increasing values of n. Does the error increases when n increases? Calculate the matrix conditioning to explain what had happened.

[Andrew Newell]

We don't do your homework for you. Have a try yourself and then tell us about any Matlab-specific issues you have.