In many cases one could spend 100 times the computational effort for an
"exact" result but find that the "exact" result is no better than the
approximation due to the limits and uncertainties with real materials as
opposed to what they "should be" or that the difference between the "exact"
and the approximate solutions are negligable.
If a more refined approach is needed- it is used, otherwise why bother?
Example- in modelling a length of wire, one can go with the following
DC: if resistance is low compared to the load-it may often be idealised to a
perfect conductor, if not, it is treated as a resistive component.
1)low frequency -treat as with DC
2)somewhat higher frequency - include inductance and possibly skin effect
3)higher yet -also include capacitance
4)higher yet- treat as a distributed parameter line
5)higher yet- it is treated as a waveguide -invoking EM field theory.
Computational effort increases from 1 to 5
Judgement/ experience determines which approach is used. Certainly one must
be aware of the assumptions used and the limits on their validity and
usefulness- That is, know what you are doing.
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