Page 210 - Schaum's Outline of Differential Equations

CHAP. 19] NUMERICAL METHODS FOR SOLVING DIFFERENTIAL EQUATIONS 193

Continuing in this manner, we generate Table 19-10.

Table 19-10

Method: MILNE'S METHOD

Problem: y' = y; y(ff) = 1
ft = 0.1
x n
True solution
py n y n Y(x) = e x
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 1.4918208 1.4918245 1.4918247

0.5 1.6487169 1.6487209 1.6487213
0.6 1.8221138 1.8221186 1.8221188

0.7 2.0137472 2.0137524 2.0137527
0.8 2.2255349 2.2255407 2.2255409

0.9 2.4595964 2.4596027 2.4596031
1.0 2.7182745 2.7182815 2.7182818