Design and Stress Analysis of Extraterrestrial ... - The Black Vault

Figure 3.25 shows the operation of normalization for a certain
function u(•). The curve U(z) is obtained from the curve u(•)
by dividing each value of the ordinates of the first curve by its
norm u(z)/ max. The second curve is normalized since its norm
U(Z)/max is equal to one.
The process of successive information will consist of determining
eigenfunction u(i+l) and eigenvalue 2 if there is an
initial approximation of function ui, based on the formula of simple
iteration
S2
SK(3.41)
r
- 2
In this formula there are two unknowns: u(i+l) and 2c(i+l)"
The method of successive approximations enables us to find the unknowr".
For this we find integral operator Kui from the function of the
initial approximation ui" The first approximation will be obtained
by normalizing the result:
- 2
W+1 I/a (.2
Since the unknown number c(i 2) is in both the function and
c(i+l)
the norm as the multiplier, it is shortened, which makes it possible
to carry out further calculations without determining it in the intermediate
stages.
After determining u(i+l) the operation is
the following approximation:
repeated and we find
tt(t+2)-'=toCUi+-, Kato-o• ( 3.113)
etc., until two neighboring approximations give sufficiently good
eigenfunction agreement.
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