JM+ ,mm+ -2d ( + ,,+- q,),
where
dmm.l = 2 d, ,
Sd, + dm+1
J = -2d,-l (, - , )
where
dm,.m = 2 dmdm-i
d, + dm-1
and
D,
d,= m = i,j,ork
Am
Eq. (8) can be expressed in a matrix form as
A* =(D
Note that Eq. (10) includes a general boundary condition using an albedo coefficient. The derivation of
boundary conditions is not presented here for brevity. Interested readers should consult Ref. (2). Using the
above formulation we can arrange the coefficients into a banded diagonal matrix. The coefficient matrix, A takes
the form seen in Figure 1. Using the Lower-Upper (LU) Decomposition approach the solution for the flux 0
is obtained.