t=0

You can set some initial value here. Alternatively, you can just draw the graph of the function with your mouse.

θ(x,0) = H^{1} norm squared :

Compute Λθ. Display factor

Compute θ

Compute θ

Compute θ

characteristic of interval.

semicircle solution.

Two semicircles.

downwards semicircle. (self similar)

Odd function.

Force even and monotone.

The blue curve you see above represents the graph of a function θ(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=-0.5, and the right side to x=0.5. The top of the white frame is θ=1, and the bottom θ=-1. The function θ is extended outside of the box as zero.

Luis Silvestre. Last update: March 25, 2014.

This is the number of points used to sample the interval [0,1]. In particular ** h = 1/(N-1) **. A large number could make the computation more accurate, but it can also make the website unresponsive if your computer cannot do the computations in time.

N = This is the time step we take at each iteration. A quantity that is too large here would make the computation inaccurate. A number that is too small would make the website unresponsive.

k = These settings are delicate. Choose the values carefully. The website may freeze if it cannot compute a time interval of 0.01 in one second.

Your computer is too slow to perform this computation in real time. Try changing the mesh settings.