Page 374 - Schaum's Outline of Differential Equations

ANSWERS TO SUPPLEMENTARY PROBLEMS 357

18.33. Method: EULER'S METHOD

Problem: / = -y; y(0) = I
y
x n n True solution
ft = 0.1 h = 0.05 ft = 0.01 Y(x) = e~ x
0.0 1.0000 1.0000 1.0000 1.0000

0.1 0.9000 0.9025 0.9044 0.9048
0.2 0.8100 0.8145 0.8179 0.8187

0.3 0.7290 0.7351 0.7397 0.7408
0.4 0.6561 0.6634 0.6690 0.6703

0.5 0.5905 0.5987 0.6050 0.6065
0.6 0.5314 0.5404 0.5472 0.5488

0.7 0.4783 0.4877 0.4948 0.4966
0.8 0.4305 0.4401 0.4475 0.4493

0.9 0.3874 0.3972 0.4047 0.4066
1.0 0.3487 0.3585 0.3660 0.3679

18.34. Method: EULER'S METHOD

Problem: y' = 2x; y(0) = 2
y
x n n True solution
h = 0.l h = 0.05 ft = 0.01 Y(x) = x 2
0.0 0.0000 0.0000 0.0000 0.0000

0.1 0.0000 0.0050 0.0090 0.0100

0.2 0.0200 0.0300 0.0380 0.0400
0.3 0.0600 0.0750 0.0870 0.0900
0.4 0.1200 0.1400 0.1560 0.1600

0.5 0.2000 0.2250 0.2450 0.2500

0.6 0.3000 0.3300 0.3540 0.3600
0.7 0.4200 0.4550 0.4830 0.4900
0.8 0.5600 0.6000 0.6320 0.6400

0.9 0.7200 0.7650 0.8010 0.8100

1.0 0.9000 0.9500 0.9900 1.0000