# Homogeneous Helmholtz Equation with Variable Coefficient

• Jun 19th 2010, 08:56 PM
KrayzBlu
Homogeneous Helmholtz Equation with Variable Coefficient
Hello,

How does one go about solving a two dimensional (or more) homogeneous helmholtz equation with a variable coefficient, i.e.

$\Delta$u(x,y) + u(x,y)*f(x,y) = 0

Where in the standard Helmholtz equation, f(x,y) = k (constant). Knowing some boundary conditions. I am at a loss as to what method to even use, having tried separation of variables, green's functions, method of characteristics. Any hints? Can this equation even be solved?

Thank You
(Bow)
• Jun 20th 2010, 04:30 AM
Jester
Is $f(x,y)$ arbitrary or does it have a specific form?
• Jun 20th 2010, 07:03 AM
KrayzBlu
Quote:

Originally Posted by Danny
Is $f(x,y)$ arbitrary or does it have a specific form?

Nope, it's arbitrary. That's a good sign... right? (Worried)
• Jun 21st 2010, 06:31 PM
KrayzBlu
It is possible that f(x,y) could be a number of step functions. Would that improve the situation?