138
tered differences for the first partial derivatives we obtain
¾(<>2M⅛) ≈ «‰)
+ 2α(τfc)
a(⅞-ι) - a(xk-ι)
2h
v(xk+ι) - v{xk~-i,}
2h
uk
h2
*⅛+ι - 2u⅛; + Vk-ι
<⅛+ι⅜+ι — ¾+ι'⅛-ι — βfc-ιVfc+ι + a,k-ιVk-ι
— ⅜+l
a2k , ɑfe z ʌ
7? + 2⅛≡<°i÷1 ^ at~t>
+ Vk
2a2
~h2
+ Vk-1
2: Leaf compartment
Leaf compartments satisfy ∂xv{t, t) = 0, which is discretized as
∂xυ{i, t)
V2 - Vi
However, because the membrane current must be accounted for from the active dy-
namics in the cable equation, we must divide through by one more h, bringing the
final expression to
^ 1 ^
h2
v2 +
— 11
h2
Vi-