Page 376 - Schaum's Outline of Differential Equations

ANSWERS TO SUPPLEMENTARY PROBLEMS 359

CHAPTER 19

19.13. Method: MODIFIED EULER'S METHOD
Problem: / = -y + x + 2; >>(0) = 2

ft = 0.1
x n
True solution
py n y n Y(x) = e~ + x+ 1
x
0.0 — 2.000000 2.000000
0.1 2.000000 2.005000 2.004837

0.2 2.014500 2.019025 2.018731
0.3 2.037123 2.041218 2.040818

0.4 2.067096 2.070802 2.070320
0.5 2.103722 2.107076 2.106531

0.6 2.146368 2.149404 2.148812

0.7 2.194463 2.197210 2.196585
0.8 2.247489 2.249975 2.249329
0.9 2.304978 2.307228 2.306570

1.0 2.366505 2.368541 2.367879

19.14. Method: MODIFIED EULER'S METHOD
Problem: y' = -y; y(0) = 1

h = 0.l
x n
True solution
py n y n Y(x) = e-*
0.0 — 1.0000000 1.0000000
0.1 0.9000000 0.9050000 0.9048374

0.2 0.8145000 0.8190250 0.8187308
0.3 0.7371225 0.7412176 0.7408182

0.4 0.6670959 0.6708020 0.6703201
0.5 0.6037218 0.6070758 0.6065307

0.6 0.5463682 0.5494036 0.5488116
0.7 0.4944632 0.4972102 0.4965853

0.8 0.4474892 0.4499753 0.4493290
0.9 0.4049777 0.4072276 0.4065697

1.0 0.3665048 0.3685410 0.3678794