Page 204 - Schaum's Outline of Differential Equations

CHAP. 19] NUMERICAL METHODS FOR SOLVING DIFFERENTIAL EQUATIONS 187

Continuing in this manner, we generate Table 19-7.

Table 19-7

Method: ADAMS-BASHFORTH-MOULTON METHOD

2
Problem: y' = y +l, y(0) = 0
h = 01
x n
True solution
py n y n Y(x) = tan x
00 — 0 0000000 0 0000090

01 — 0 1003346 0 1003347
02 — 0 2027099 0 2027100

03 — 0 3093360 0 3093363
04 04227151 0 4227981 0 4227932

05 0 5461974 05463149 0 5463025
06 0 6839784 06841611 0 6841368

07 0 8420274 08423319 0 8422884
08 1 0291713 1 0297142 1 0296386

09 1 2592473 1 2602880 1 2601582
10 1 5554514 1 5576256 1 5574077