the solution of elliptic/hyperbolic equations

Olek

Dear Forum People!

I am trying to solve the set of following equations in 1D

1. partial(u)/partial(x) = f1(c) 2. partial(c)/partial(t) + u partial(c)/partial(x) = f2(c)

As it is seen the flow is incompressible and inviscous. The first equation is continuity equation with source that depends on the concentration (elliptic as far as i know). The second equation is the convection equation (first order wave equation) also with concetration source.

Do somebody have some idea what is the best and the easiest way to solve those equations. I was thinking about a relaxation method (FDM) but I am not sure how the second equation behaves well enough when solved with this method.

I am grateful for any help!

Olek