1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: P.d.e problem

  1. Nov 26, 2005 #1
    we are given the laplacian:
    (d^2)u/(dx^2) + (d^2)u/(dy^2) = 0 where the derivatives are partial. we have the B.C's
    u=0 for (-1<y<1) on x=0
    u=0 on the lines y=plus or minus 1 for x>0
    u tends to zero as x tends to infinity.

    Using separation of variable I get the general solution

    u = (ax+b)(cy+d) + sum over k of (Ak*sinky + Bk*cosky)*(Ck*exp(kx) + Dk*exp(-kx))

    where a,b,c,d,Ak,Bk,Ck,Dk are constants. We can then say that Ck = 0 from B.C's, and I also think that we can say that a=b=c=d=0 as well (but I am not sure). I'm having trouble imposing the rest of the B.C's. the final solution is
    u=sum over m of [Am*cos(m*Pi*y/2)*exp(-(m*Pi*x/2)

    thanks very much
  2. jcsd
  3. Nov 27, 2005 #2


    User Avatar
    Science Advisor

    Since [itex]cos(\frac{n\pi}{2})= cos(-\frac{n\pi}{2})= 0[/itex] for n any positive integer, you can satisfy the boundary condition u(x,y)= 0 for |y|= 1 by choosing [itex]k= -\frac{n\pi}{2}[/itex]. Of course, the the coefficient of sin(kx) must be 0 for all k for the same reason.
  4. Nov 27, 2005 #3
    Hi, thanks for the clarification. i'm now stuck on the next bit: determining the coefficients. I'm not sure what limits to integrate between, and keep getting all of my coefficients equal to zero.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook