# Introductory PDE (diffusion equation)

1. Sep 24, 2009

### compliant

1. The problem statement, all variables and given/known data

$$u_t = -{{u_{x}}_{x}}$$
$$u(x,0) = e^{-x^2}$$

2. Relevant equations

3. The attempt at a solution
The initial state is a bell curve centred at x=0. The second partial derivative of u at t=0 is $${4x^2}{e^{-x^2}}$$, which is a Gaussian function, which means nothing to me other than its bell-curved shape.

The solution is http://www.orcca.on.ca/~reid/Courses//AMath315/Fall2009/Solutions/Assign1-Fab.pdf" (the top graph), but I just want to know how on earth he (my prof who wrote up said solutions) came up that graph for time t + delta t, and what on earth he means by whatever it is he wrote down there.[tex]

Last edited by a moderator: Apr 24, 2017
2. Sep 29, 2009

bump.