Changes between Version 7 and Version 8 of u/ticket

Timestamp:

11/18/14 15:47:42 (10 years ago)

Author:

Erica Kaminski

Comment:

—

u/ticket

@@ -46 +46 @@
 [[latex($\phi_{r+1,z} (\frac{1}{2 r \triangle r} + \frac{1}{\triangle r ^2}) + \phi_{r-1,z} (\frac{1}{\triangle r ^2} - \frac{1}{2 r \triangle r }) + \phi_{r,z}(\frac{-2}{\triangle r ^2}) + ( " ")$)]]
 
-Putting into the Poisson equation, and moving the delta r's over:
+Putting into the Poisson equation, and moving the delta r^2^'s over:
 
-[[latex($\phi_{r+1,z}(\frac{\triangle r}{2 r } + 1) + (1 - \frac{\triangle r}{2 r}) + \phi_{r,z+1} + \phi_{r,z-1} - 4 \phi_{r,z}$)]]
+[[latex($\phi_{r+1,z}(\frac{\triangle r}{2 r } + 1) + \phi_{r-1,z}(1 - \frac{\triangle r}{2 r}) + \phi_{r,z+1} + \phi_{r,z-1} - 4 \phi_{r,z} = (4 \pi G\rho_{r,z})\triangle r ^2$)]]
+
+Therefore the "modified" 2D 5-point stencil has the following coefficients in 2.5 D:
+
+[[latex($[{(\frac{\triangle r}{2 r } + 1), (1 - \frac{\triangle r}{2 r}), 1, 1, -4}]$)]]