- #1

hunt_mat

Homework Helper

- 1,741

- 25

[tex]

a\frac{\partial^{2}\phi}{\partial y^{2}}+\frac{\partial^{2}\phi}{\partial u^{2}}+b\frac{\partial\phi}{\partial u}=-ce^{-y^{2}}

[/tex]

Where a,b and c are constants. Along with the conditions:

[tex]

\phi (y,0)=\frac{\partial\phi}{\partial u}(y,0)=0,\quad\lim_{y\rightarrow\infty}\phi (y,u)=\lim_{y\rightarrow\infty}\frac{\partial\phi}{\partial y}(y,u)=0

[/tex]

I have tried the usual approach using Laplace transforms but I got into a horrible mess with looking at the particular solution which involved horrible things like complimentary error functions and the like. As well as that mess, computing the inverse transforms were waay waay to hard as I had to look at [tex]\sqrt{\alpha s^{2}+\beta s}[/tex] where s was my Laplace transform variable and I had no idea what to do regarding them so I dropped that method.

My current idea is to use Greens functions but I don't know a great deal about them and was after some advice.

Regards

Mat