Page 223 - Schaum's Outline of Differential Equations

206 SOLVING SECOND-ORDER DIFFERENTIAL EQUATIONS [CHAP. 20

20.11. Use the Adams-Bashforth-Moulton method to solve y"-y = x; y(0) = 0, /(O) = 1 on the interval [0, 1]
with/; = 0.1.
It follows from Problem 20.1 that/(jc, y,z) = z and g(x, y, z)=y + x and from Table 20-3 that
XQ = 0 y 0 = 0 z a = 1
jd=0.1 y 1 = 0.1003333 Zi = 1.0100083

x 2=0.2 y 2 = 0.2026717 z 2 = 1.0401335

x = 0.3 y, = 0.3090401 z, = 1.0906769
Using (20.6), we compute

Then using (20.5), we compute