how do you solve a laplace equation given that u(x,0) =0, u(x,1) = sin ^3 (pi x)

u(x,y)=0 and u(1,y) =0 for 0<x<1, 0<y<1?

i got the final answer of sum {sin ^3(pi x) sinh(n pi y)} over (sinh(pi x))

but this seems to look wrong.

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- May 10th 2011, 09:27 AMalexandrabel90laplace
how do you solve a laplace equation given that u(x,0) =0, u(x,1) = sin ^3 (pi x)

u(x,y)=0 and u(1,y) =0 for 0<x<1, 0<y<1?

i got the final answer of sum {sin ^3(pi x) sinh(n pi y)} over (sinh(pi x))

but this seems to look wrong. - May 10th 2011, 09:35 AMTheEmptySet
I think you have a typo. Did you mean

Quote:

u(x,y)=0

Your answer should not have trig functions rasied to any power as they are not part of the basis!

Hint 1:

Using the above the only terms that will survive when you expand the x's with will the two given above.

Please post what you have done. - May 10th 2011, 09:46 AMalexandrabel90
ya i meant u(o,y) = 0.

- May 10th 2011, 09:59 AMalexandrabel90
Attachment 21533

this is my working with the help that you gave. im still confused with how to find the solution :( - May 10th 2011, 10:35 AMTheEmptySet
So you have

Now using the boundary condition we have

Now using the inner product we can solve for the constants. Multiply both sides by

and integrate you will need a 2 in front of your integral to make the set orthonormal.

The left hand side is only non zero when n=1 or n=3

This gives

all of the other c's are zero so the sum only contains two terms and gives

- May 10th 2011, 11:14 AMalexandrabel90
i think c1 and c2 should be both multiplied by 2 right?

- May 10th 2011, 01:34 PMTheEmptySet