Automatic analysis circuits concentrated constant electrical workers
1) Typology of automatic analysis of the circuits:
to) Transformed of Laplace practically made unusable in how much not always easy to find the transformed ones
b) Algorithms of Euler (finite-difference method)
2) local Error:
One obtains developing in series of Taylor, so that from x(tk) and from its derivatives in tk the value of x(t can be determinedk 1), the local error is function of the term of the development which it is arrested to us. In short it indicates for a single step of the procedure which difference is between the real value and the deliberate value.
3) Order of an algorithm:
It is the exponent of the interval of sampling in the diminished local error of 1.
4) Error total:
In correspondence to the step (k 1)_esimo it is worth 
where xk 1 it is the value obtained with the finite-difference method
after k 1 steps of integration to leave from the value begins them
exact x0 = x(t0).
It diminishes if the sampling interval diminishes and if the trapezial algorithm is used.
5) Algorithm of direct Euler:
The derivative comes reduced to the relationship increases carried out them on one series of second extracted champions every every T,
if 
has:
It is an algorithm of 1° the order, in the equivalent outline is only a generator.
6) Algorithm of indirect Euler:
The derivative comes reduced to the relationship increases carried out them on one series of second extracted champions every every T,
if has:
It is an algorithm of 1° the order, in the equivalent outline there is a generator and a resistore.
7) Algorithm of trapezial Euler:
The derivative comes reduced to the relationship increases carried out them on one series of second extracted champions every every T,
if has:
It is an algorithm of 2° the order, in the equivalent outline there is a generator and a resistore.
8) Outline equivalent for the inducer with the algorithm of direct Euler:
For the inducer 
therefore from the is had obtains 
and therefore
rielaborando 
therefore has a generator of current
of 
value if instead 
in the
equivalent circuit were had would have one conductance.
9) Analyses of a circuit with the finite-difference method:
The algorithm is chosen, finds the circuit equivalent of L and C with that algorithm and is replaced in the circuit originates them, keeps in mind who in designing the circuit equivalent of a member, to the largenesses reported to the previous state is necessary to associate a generator whose type must guarantee the homogeneity of the equation.
10) Change of scale of the frequency and its effect on the members:
Draft of a normalization that concurs to set up intervals more narrow than variations of the frequencies therefore makes so that the standardized frequency is 1. For the single members it is had:
11) Change of scale of the stiffnesses:
Prestabilita amount R 0 comes altered the stiffnesses ofone :
12) Change of scale of the stiffnesses and the frequencies:
