t=0

Initial value for u:

Initial value for u_{t}:

Dirichlet condition: u(0,t)=u(1,t)=0.

Neumann condition: u

Solution to the Wave equation u_{tt} = u_{xx}.:

The coordinate x varies in the horizontal direction. It goes from x=0 on the left side of the white frame to x=PI on the right side. The top of the white frame represents u=1, and the bottom u=-1. The level u=0 is right in the middle.

When you click "Start", the graph will start evolving following the wave equation.

You can edit the initial values of both u and u_{t} by clicking your mouse on the white frames on the left.

Note that the function does NOT become any smoother as the time goes by. It is also interesting to see how the waves bounce back from the boundary.

Luis Silvestre. May 16, 2013.

The solution to the wave equation is computed using separation of variables.

Check also the other online solvers