- #1
sachi
- 75
- 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
(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