Rit (Vísindafélag Íslendinga) - 01.06.1946, Side 27

27
lar cases as this one, I find often more convenient to calculate
dy
y and ~ for an appropriate value of the £ which I have
found, from suitable approximate equations, to be not far
from thecorrect value.In the case concernedthe mean of ífrom
(46) and (47) is t = 0.631, and for this value of t I
find, for k = 8, from (37a) ij = — 0.01796 and from (38a)
dy
~ = 2.5030, and consequently y = 0 for / == 0.631 — 0.0072
= 0.6238. Brainerd and Weygandt give t = 0.625 (scaled
from curves), and t= 0.637 - (calculated) °).
If t = 150° the calculations become more difficult. From
(46) we get the positive value of t, t = 1.25 while from
(47) t = 1.03.
The difference between these values is double as com-
pared with thaí when t = 0, which fact indicates that we
have to reckon with larger k than in case of t = 0, if
we shall expect to attain a similar accuracy. However,
this is not surprising because t found now is nearly double
that previously found. Using the mean £=1.14 I get from
(37a) and (38a) for k = l, ylM= 0.0355, = — 1.425.
whence £ = 1.169 for y = 0.
Whereas from (41) and (43) I get for k = 8
dy..,
yx 14 = 0.0657, --— = — 1.327 corresponding to £=1.189
’ dt
for y = 0.
The difference is still 2 in second decimal place. Hence
it becomes apparent that we have to choose k rather large,
if we shall, for instance, have 4 decimals correctly. In such
a case it is, therefore, usually more preferable to use (18)
where i\ is of similar magnitude as s. The method of
asymptotic differentiation will of course, give the same