Page 381 - Schaum's Outline of Differential Equations

364 ANSWERS TO SUPPLEMENTARY PROBLEMS

19.25. Method: ADAMS-BASHFORTH-MOULTON METHOD

Problem: / = -}>; y(0) = 1
ft = 0.1
x n
True solution
py n y n Y(x) = e~ x
0.0 — 1.0000000 1.0000000

0.1 — 0.9048375 0.9048374
0.2 — 0.8187309 0.8187308
0.3 — 0.7408184 0.7408182

0.4 0.6703231 0.6703199 0.6703201

0.5 0.6065332 0.6065303 0.6065307
0.6 0.5488136 0.5488110 0.5488116
0.7 0.4965869 0.4965845 0.4965853

0.8 0.4493302 0.4493281 0.4493290

0.9 0.4065706 0.4065687 0.4065697
1.0 0.3678801 0.3678784 0.3678794

19.26. Method: ADAMS-BASHFORTH-MOULTON METHOD

Problem

h = 0.2
x n
True solution
py n y n Y(x) = x-y/9 + lnx 2
1.0 — 3.0000000 3.0000000

1.2 — 3.6722028 3.6722045
1.4 — 43541872 43541901

1.6 — 5.0444406 5.0444443
1.8 5.7419118 5.7418465 5.7418514

2.0 6.4455861 6.4455489 6.4455549