Page 208 - Schaum's Outline of Differential Equations

CHAP. 19] NUMERICAL METHODS FOR SOLVING DIFFERENTIAL EQUATIONS 191

Table 19-8

Method: MILNE'S METHOD

Problem: y' = y~x; y(0) = 2
h = 0.1
x n
True solution
py n y n Y(x) = e +x+l
x
0.0 — 2.0000000 2.0000000

0.1 — 2.2051708 2.2051709
0.2 — 2.4214026 2.4214028
0.3 — 2.6498585 2.6498588

0.4 2.8918208 2.8918245 2.8918247

0.5 3.1487169 3.1487209 3.1487213
0.6 3.4221138 3.4221186 3.4221188
0.7 3.7137472 3.7137524 3.7137527

0.8 4.0255349 4.0255407 4.0255409

0.9 4.3595964 4.3596027 4.3596031
1.0 4.7182745 4.7182815 4.7182818

Continuing in this manner, we generate Table 19-9.