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2. Leaf compartment: the most distal compartment of a leaf
3. Parent compartment (non-soma): compartment N of a child branch whose
parent is another branch
4. Parent compartment (soma): compartment N of a root branch
5. Branch compartment: the first compartment of a parent branch
6. Soma
For clarity in the following derivations I will drop the branch subscript b and in-
stead will indicate quantities by their compartment index k. Thus here α⅛ should be
interpreted as α(a⅛), and similarly for u⅛.
1: Interior compartment
From the main cable equation we compute the partial derivative term as
¾(α2(^)¾∙υ) = α2(τ)‰ + 2a(x)axvx.
Using the standard discretization scheme for the second partial derivative and cen-