Page 386 - Schaum's Outline of Differential Equations
P. 386
ANSWERS TO SUPPLEMENTARY PROBLEMS 369
20.27. Method: MILNE'S METHOD
Problem: /' + y = 0; y(0) = 1 , /(O) = 0
ft = 0.1
x n
True solution
py n PZ n y n 7 ^•n Y(x) = cos x
0.0 — — 1.0000000 0.0000000 1.0000000
0.1 — — 0.9950042 -0.0998333 0.9950042
0.2 — — 0.9800666 -0.1986692 0.9800666
0.3 — — 0.9553365 -0.2955200 0.9553365
0.4 0.9210617 -0.3894153 0.9210611 -0.3894183 0.9210610
0.5 0.8775835 -0.4794225 0.8775827 -0.4794254 0.8775826
0.6 0.8253369 -0.5646395 0.8253358 -0.5646426 0.8253356
0.7 0.7648437 -0.6442148 0.7648423 -0.6442178 0.7648422
0.8 0.6967086 -0.7173535 0.6967069 -0.7173564 0.6967067
0.9 0.6216120 -0.7833245 0.6216101 -0.7833272 0.6216100
1.0 0.5403047 -0.8414690 0.5403024 -0.8414715 0.5403023
20.28. predictors:
correctors:
20.29.
where
