How can I find the Numerical Solution of the fourth order PDE?

Here are the PDE, Initial and Boundary conditions:

I found the analytical solution using the Separation of variables method. I am trouble having finding the Numerical Solution. How can I do this in MATLAB?

[Torsten]

By writing your equation as a system of two equations

du/dt = v
dv/dt = -d^4u/dx^4,

discretizing the spatial derivative and solving the resulting system of ordinary differential equations using ODE15S.

Best wishes

Torsten.