The name is absent

where v_τ is the voltage at the transition compartment. By (4.6) this implies

(4.8)

Although the implementation above is only first-order accurate, it can be improved
to second-order accuracy as described in §A.2. However, all the results in this thesis
were produced using the first-order scheme.

Discretizing the ∂_xx terms in the above systems and substituting in for v_r we
arrive at expressions for the voltages at the compartments adjacent to the transition
compartment:

V²_s - ^2vs + VT

(ʌʃ)²

v² — 2v¹ + ɪvɪ 4- ɪv^
s           ' 2 s ' 2 ^vW

(∆x)²

v² — -vɪ + l∙v^^f,u

^vs 2 S ' 2 W

(Ax)²

lvɪ — -v^^w 4

2 S 2^vw ~

(Ax)²

This reveals the coupling between these two systems. Using the Hines ordering, I now

discretize (4.2)-(4.4) and the conditions given in (4.5) and (4.7) to arrive at

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