The name is absent

92

possible to solve for. In integrating equation 5.9 numerically as done by Lamb and Simon
[69], there is error in the calculation of the Bessel functions by the computer. As a result,
it is much more convenient and straightforward to solve the entire network numerically in
the first place, rather than from an analytic solution.

Normally numerical solutions are used as discrete approximation to a continuous prob-
lem. They are useful in many cases where analytical solutions cannot be derived, because of
either complex problem geometry or in the case of nonlinear problems. Where they exist,
analytical solutions can act as a check on the accuracy of the numerical solution. To in-
crease the accuracy of a numerical solution for a continuous problem, the discretization is
made finer in space and time, requiring more computational power. However, coupled pho-
toreceptors are discrete elements which can be considered isopotential, so a spatial finite-
difference scheme is able to capture the discrete topology of the rod network exactly. There-
fore a numerical finite difference integration scheme that is easy to implement with a com-
puter is an ideal way to solve for the voltage in the rod network.

The one dimensional heat equation can be discretized as follows:

(5.10)

(5.11)

where v_n represents the voltage at photoreceptor n, and i_n represents the current injected
into photoreceptor n. This scheme can be directly realized from the circuit diagram for the
rod, shown in figure 5.6. This scheme can be written in vector / matrix form, with tridiagonal

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