Changes between Version 3 and Version 4 of u/ticket

Timestamp:

11/18/14 15:19:03 (10 years ago)

Author:

Erica Kaminski

Comment:

—

u/ticket

@@ -34 +34 @@
 [[latex($ \triangledown ^2_{(2.5D)} = \frac{1}{r}\frac{\partial }{\partial r}(r\frac{\partial}{\partial r}) + \frac {\partial ^2}{\partial z ^2} = \frac{1}{r} [\frac{\partial}{\partial r} + r \frac{\partial^2}{\partial r ^2}] + \frac{\partial ^2}{\partial z^2}$)]]
 
-Expanding out and putting into Poisson equation, 
+Multiplying the 1/r through the first term, and putting these derivatives into Poisson's equation gives, 
 
-[[latex($  \frac{1}{r}\frac{D }{Dr} \phi_{r,z} + \frac{D^2}{D r^2}\phi_{r,z} + \frac{D^2}{Dz^2} \phi_{r,z} = \rho_{r,z}$)]]
+[[latex($  \frac{1}{r}\frac{D }{Dr} \phi_{r,z} + \frac{D^2}{D r^2}\phi_{r,z} + \frac{D^2}{Dz^2} \phi_{r,z} = 4 \pi G \rho_{r,z}$)]]
+
+where the capital D's now represent the derivative ''operators''. Putting the operators into their discretized, 2nd-order forms gives for the LHS:
+
+[[latex($  \frac{1}{r}\frac{D }{Dr} \phi_{r,z} + \frac{D^2}{D r^2}\phi_{r,z} + \frac{D^2}{Dz^2} \phi_{r,z} = 4 \pi G \rho_{r,z}$)]]
 
 
-