[TurbJet]

I am trying to solve a simple diffusion equation



where a & b are some given constant, for the sake of simplicity, let's say they are both 1, and the spatial domain is [-1, 1] with periodic BC, the initial condition is numerical delta function .

Solving this by simply using a naive schemes:



When I compare results from different time step sizes, the smaller the time step size, the more diffusive it appears to be: the wave, or the delta function, spreads out much faster in space (smoothed out) when advance in time, with smaller time step size. But according to the scheme, lowering time step size will obviously reducing the 2nd-order derivative, i.e., the diffusion term, as well, thus it should have lead to less diffusion for smaller .

So where does this conflict come from?

Thx!