Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

Sec. 5] Numerical Integration of Ordinary Differential Equations 389
We obtain i/4 = y4 = 3.3590 (in this approximate number the first three
decimals are guaranteed).
Similarly we calculate the values of y^ and y^. The results are given in
Table 2.
Thus, we finally have
y (1.5) = 4.74.
4. Adams' method. To solve (1) by the Adams method on the basis of
the initial data */(x = ) /o we in some
g way find the following three values
of the desired function y (x):
[these three values may be obtained, for instance, by expanding y (x) in a
power series (Ch IX, Sec. 16), or they may be found by the method of successive
approximation (1), or by applying the Runge-Kutta method (2)
and so forth].
With the help of the numbers X Q , x it * 2 , x t and */ . y lt yzt ys we calculate