Draw arbitrary functions with your mouse and see them evolve by the heat equation, or any other finite different scheme of your choice.


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.

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.

Check also the other online solvers