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PoissonPlusHydro

-              v2
+              v3
 where [[latex($\vec{u}$)]] is vector of fluid variables, [[latex($\vec{F}$)]] is their fluxes, and [[latex($\vec{S}$)]] is the source-term vector.
+To solve this system of equations, we can employ operator splitting, which is analagous to the procedure for splitting the higher dimensional Euler equations (as I did for 2D -- see wiki page).
+It is basically as follows, first solve the homogenous equations,
+[[latex($\vec{u}_t + \vec{F}(\vec{u})_x = 0$)]]
+with initial condition for the grid,
+[[latex($\vec{u}(x,0) = \vec{u}_i ^0$)]]
+over a time-step dt (found by usual CFL condition for upwind Godunov scheme). This gives the solution,
+[[latex($\vec{u}^{n+1/2}$)]]
+Next, solve the equation for the source-term,
+[[latex($\frac{d}{dt}\vec{u} = \vec{S}(\vec{u})$)]]
+with initial condition
+[[latex($\vec{u}(x,0) = \vec{u}^{n+1/2}$)]]
+This gives the solution for the complete time-step,
+[[latex($\vec{u}^{n+1}$)]]
+Given the ODE's for the 'source' step only involve equations for momentum and energy, we conclude that only u and E change over this step (density does not).
+Thus, a schematic is as follows,
+Hydro step [[latex($\rightarrow$)]] [[latex($\vec{u} = <\rho^{n+1/2}, u^{n+1/2}, E^{n+1/2}>~\rightarrow$)]]
+Source step [[latex($\rightarrow$)]] [[latex($\vec{u} = <\rho^{n+1/2}=\rho^{n+1}, u^{n+1}, E^{n+1}>$)]]