Page 380 - Schaum's Outline of Differential Equations

ANSWERS TO SUPPLEMENTARY PROBLEMS 363

19.23. Method: ADAMS-BASHFORTH-MOULTON METHOD

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

0.1 — 1.1051708 1.1051709
0.2 — 1.2214026 1.2214028

0.3 — 1.3498585 1.3498588
0.4 1.4918201 1.4918245 1.4918247

0.5 1.6487164 1.6487213 1.6487213
0.6 1.8221137 1.8221191 1.8221188

0.7 2.0137473 2.0137533 2.0137527
0.8 2.2255352 2.2255418 2.2255409

0.9 2.4595971 2.4596044 2.4596031
1.0 2.7182756 2.7182836 2.7182818

19.24. Method: ADAMS-BASHFORTH-MOULTON METHOD

Problem: / = -y + x + 2; y(0) = 2
h = 0.l
x n
True solution
py n y n Y(x) = e~ + x+l
x
0.0 — 2.000000 2.000000

0.1 — 2.004838 2.004837
0.2 — 2.018731 2.018731

0.3 — 2.040818 2.040818
0.4 2.070323 2.070320 2.070320

0.5 2.106533 2.106530 2.106531
0.6 2.148814 2.148811 2.148812

0.7 2.196587 2.196585 2.196585
0.8 2.249330 2.249328 2.249329

0.9 2.306571 2.306569 2.306570
1.0 2.367880 2.367878 2.367879