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scratchpad5

-              v18
+              v19
 $T_0 +  \displaystyle \sum_{\parallel, \perp} \left [ \alpha_0 T^{\lambda+1}_0 +  \displaystyle \sum_{\pm j} \alpha_{\pm j} T^{\lambda+1}_{\pm \hat{j}} +  \sum_{\pm i, \pm j,i \ne j} \alpha_{\pm i, \pm j} T^{\lambda+1}_{\pm \hat{i} \pm \hat{j}} \right ] = T'_0$
+=== Boundary Terms ===
+==== Explicit ====
+Here, the boundary terms are quite straightforward.  We can just use the regular boundary conditions (or user specified boundary conditions).  The only difficulty arises when trying to set a heat flux since this involves solving a non-linear equation.  One solution is to set the heat flux explicitly - instead of indirectly through the temprature.   Then use extrapolating (pr reflecting) BC's for temperature so there is no heat flux initially calculated along the boundary - and then add in the flux in a separate step.
+==== Implicit ====
+For reflecting - or extrapolating boundary terms, we can just transfer the coefficients for the boundary terms and apply them to their mirror zone.  The only thing to be careful about - is that for the anisotropic case, there are corner zones who's coefficients may need to be transferred twice.  This just requires transferring corner zone coefficients, to edge zones, before transferring edge zones, to the central cell in the stencil.