# Numerical methods for $u_t+c u_x= \frac{-c}{x}u$?

I am looking for possible numerical methods to solve the PDE $$u_t+c u_x= \frac{-c}{x}u$$

I am particularly interested in a Finite elements method, although I am also curious if you can expose some other methods.

• It looks like there is an analytic solution here, if that's of interest. Jun 20 at 19:40
• Specifically, you can use the method of characteristics I assume. But you need to state the domain of possible $x$ values, and what you want to happen at $x=0$. Jun 21 at 0:48