# Problem in Fourier series and Pdes

Discussion in 'Undergraduate Math' started by junoexpress, Nov 11, 2011.

1. ### junoexpressGuest

Hi,

I am working on a problem from Churchill and Brown "Fourier series and
PDEs", 7th ed.

Problem is to solve the heat eqn:
(i) U_t = k * U_x,x -inf<x<+inf, t>0

Given the initial temp distbn:
f(x) = 1 if x>0, 0 if x<0

I work through the problem and get the soln:
U(x,t) = 1/2 * (1 - Erf[ x / (2*sqrt(k*t)] ) for t>0
the book gets the same soln but has a plus sign between the two terms.

Does anyone know offhand which soln is correct or if the book is in
error on this problem. I've gone through it several times and cannot
find an error on my part.

Thanks,
Matt

junoexpress, Nov 11, 2011

2. ### Stephen Montgomery-SmithGuest

The easiest thing is to consider the limit of U(x,t) as t->0.
Remember Erf[x]->1 as x->oo, and -1 as x->-oo. It looks to me like
Churchill and Brown are correct, and you are incorrect.

Stephen Montgomery-Smith, Nov 12, 2011

3. ### biofilmGuest

what does the effect of + or a - have ? increases or decreases?

biofilm, Nov 12, 2011
4. ### biofilmGuest

what is min and max value of the + or the - and does that make sense ?

biofilm, Nov 12, 2011
5. ### junoexpressGuest

Yes, that makes sense. Thank you for the observation ;>)

junoexpress, Nov 12, 2011