The name is absent

141

6: Soma

The soma satisfies the three conditions (2.21) and (2.22), and hence for the dth
root we write

7Γ

^D л ⅞(θ)⅛¾(θι ^) ~ ^_so∏ιa

A.2 Second-order Approximations of Boundary Conditions

The derivations in the previous section describe the implementation of the codes as
used to generate the results in this thesis, but they involve mixed orders of accuracy.
The interior nodes are computed to second-order accuracy, but the boundary nodes
(and the junction nodes) are only computed using first-order accurate schemes.

Second-order accuracy for the boundary conditions can be obtained by implement-
ing an appropriate one-sided finite difference scheme (Niebur and Niebur, 1991). For
example, the sealed end condition ∂_xv(f,t) — θ can be discretized as

л ιo ≠∖ -3v₁+4v₂-v₃

MM) ≈---—---,

and similarly this may be applied to the junction conditions to recover second-order
accuracy across the whole spatial grid.

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