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Concluding Remarks on Unequal Spatial Intervals

The question arises of how low an N value it is possible to work with and still get good results. The simulation package DigiSim due to Rudolph and Feldberg [482] routinely uses as few as 14 and is able to achieve sufficient accuracy in the current. This depends on one s definition of sufficient . If 0.1% accuracy is wanted, about 40 points in space might be optimal. [Pg.110]

Clearly also, in order to choose a suitable set of parameters, one must know the requirements before the simulation. If some homogeneous rate constant changes during a series of program runs (for example one in which such a rate constant is searched for), then the grid parameters should change. This makes adaptive grids more useful. These are described below. [Pg.110]

As for the choice between direct discretisation on an arbitrarily spaced grid or the formulae for the semi-transformed or the transformed diffusion equation, the present author now inclines towards the first of these. Formulae for the derivatives on arbitrarily spaced points are given in Chap. 3 and Appendix A, and the general subroutine U DERIV is referred to in Appendix C. [Pg.111]

Just as space can be divided into unequally spaced intervals, so might time also be unevenly divided. As with spatial intervals, there is the choice between discretising on an uneven time grid or using a transformation to a new time scale. Since, except for BDF methods, one usually differentiates with respect to time using only two time points (levels), transformation does not make sense here. [Pg.111]

The following is often used. We choose exponentially increasing time intervals over some period r, which may be the total simulation period, a pulse duration or (see below) a single whole time interval to be subdivided. The period is divided into Al intervals of length 8tk, k 1,AI. Assume the [Pg.111]

As for the choice between direct discretisation on an arbitrarily spaced grid or the formulae for the semi-transformed or the transformed diffusion equation, the present [Pg.132]


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11.7 Concluding Remarks

Remarks

Unequal

Unequal intervals

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