Page 196 - Schaum's Outline of Differential Equations

CHAP. 19] NUMERICAL METHODS FOR SOLVING DIFFERENTIAL EQUATIONS 179

Table 19-1

Method: MODIFIED EULER'S METHOD
Problem: y' = y- x- (Q) = 2
y
ft = 0.1
x n
True solution
py n y n Y(x) = (f + x + 1
0.0 — 2.0000000 2.0000000

0.1 2.2000000 2.2050000 2.2051709
0.2 2.4155000 2.4210250 2.4214028
0.3 2.6431275 2.6492326 2.6498588

0.4 2.8841559 2.8909021 2.8918247

0.5 3.1399923 3.1474468 3.1487213
0.6 3.4121914 3.4204287 3.4221188
0.7 3.7024715 3.7115737 3.7137527

0.8 4.0127311 4.0227889 4.0255409

0.9 4.3450678 4.3561818 4.3596031
1.0 4.7017999 4.7140808 4.7182818

(19.3), we compute

Continuing in this manner, we generate Table 19-2. Compare it to Table 18-3.