I'm trying to solve a greens function problem for the laplace equation using fourier series transformations.

d^4*Wn(x)/dx^4 - 2v*d^2*Wn(x)/dx^2+v^4*Wn(x) = -fn(x) is the problem I'm solving.

Bounday conditions are

0 < x < infinity

w(0,y) = 0

d^2w(0,y)/dx^2 = 0

The general solution to the homogenous problem is given by

Wn(x) = c1(x)*exp(v*x)+c2(x)*exp(-v*x)+c3(x)*x*exp(v*x)+c4(x)*x*exp(-v*x)

I solved for c1 prime, c2 prime, c3 prime, c4 prime using Cramers rule, and after multiplying above, I get the simplified version of line 1 in my code.

To get c1,c2,c3,c4 I simply integrated which you see on line 2. D1+D2+D3+D4 are the constants of each integration that I need to solve for.

Because of 0<x<infinity, exp(v*x) and x*exp(v*x) is unbounded as x approaches infinity. To fix this, we set c1 + D1 = 0 and c3 + D3 = 0. In other words, D1 = -c1, D3 = -c3 and they are both integrals from 0 to infinity.

I then try to use maple for the remaining two boundary conditions to solve for D2 / D4, plug them back into my W(n) function, and eventually plot it.

Hope this explanation helps.

I'm trying to solve a greens function problem for the laplace equation using fourier series transformations.

d^4*Wn(x)/dx^4 - 2v*d^2*Wn(x)/dx^2+v^4*Wn(x) = -fn(x) is the problem I'm solving.

Bounday conditions are

0 < x < infinity

w(0,y) = 0

d^2w(0,y)/dx^2 = 0

The general solution to the homogenous problem is given by

Wn(x) = c1(x)*exp(v*x)+c2(x)*exp(-v*x)+c3(x)*x*exp(v*x)+c4(x)*x*exp(-v*x)

I solved for c1 prime, c2 prime, c3 prime, c4 prime using Cramers rule, and after multiplying above, I get the simplified version of line 1 in my code.

To get c1,c2,c3,c4 I simply integrated which you see on line 2. D1+D2+D3+D4 are the constants of each integration that I need to solve for.

Because of 0<x<infinity, exp(v*x) and x*exp(v*x) is unbounded as x approaches infinity. To fix this, we set c1 + D1 = 0 and c3 + D3 = 0. In other words, D1 = -c1, D3 = -c3 and they are both integrals from 0 to infinity.

I then try to use maple for the remaining two boundary conditions to solve for D2 / D4, plug them back into my W(n) function, and eventually plot it.

Hope this explanation helps.

I'm getting the following errors now. I know D1 and D3 already, so that is why I entered them in manually. I use the other two boundary conditions (BC1,BC2) to solve for D2 and D4. Help would be greatly appreciated.

Download project2.mwproject2.mw

I'm getting the following errors now. I know D1 and D3 already, so that is why I entered them in manually. I use the other two boundary conditions (BC1,BC2) to solve for D2 and D4. Help would be greatly appreciated.

Download project2.mwproject2.mw

Thank you so much for the help!

Thank you so much for the help!