Draw arbitrary functions with your mouse and see them evolve.

t=0

Initial value

You can set some initial value here. Alternatively, you can just draw the graph of the function with your mouse.
u(x,0) =

Boundary conditions

You can choose the type of boundary condition here.
Dirichlet condition: u(0,t)=u(1,t)=0.
Neumann condition: ux(0,t)=ux(1,t)=0.

Iteration scheme

You can specify here the finite difference iteration scheme. instructions.
u[i]=

Maximum time

The evolution will stop when the time t reaches the value below.
MAX t =

The blue curve you see above represents the graph of a function u(x,t) for a fixed value of t.

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

When you click "Start", the graph will start evolving following the finite difference scheme specified above.

Luis Silvestre. Last update: July 19, 2013.

Check also the other online solvers