Page 382 - Schaum's Outline of Differential Equations

ANSWERS TO SUPPLEMENTARY PROBLEMS 365

19.27. Method: MILNE'S METHOD

Problem: / = -y + x + 2; y(0) = 2
ft = 0.1
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 2.106531 2.106531
0.6 2.148814 2.148811 2.148812

0.7 2.196588 2.196585 2.196585
0.8 2.249331 2.249329 2.249329

0.9 2.306571 2.306570 2.306570
1.0 2.367881 2.367879 2.367879

19.28. Method: MILNE'S METHOD

Problem: y' = -y; y(0) = 1

h = 0.l
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 0.6703225 0.6703200 0.6703201

0.5 0.6065331 0.6065307 0.6065307

0.6 0.5488138 0.5488114 0.5488116
0.7 0.4965875 0.4965852 0.4965853
0.8 0.4493306 0.4493287 0.4493290

0.9 0.4065714 0.4065695 0.4065697

1.0 0.3678807 0.3678791 0.3678794