Page 378 - Schaum's Outline of Differential Equations

ANSWERS TO SUPPLEMENTARY PROBLEMS 361

19.18. Method: RUNGE-KUTTA METHOD

Problem: / = y + x + 2;y(0) = 2
ft = 0.1 True solution
x n
y n Y(x) = e~ +x+l
x
0.0 2.000000 2.000000

0.1 2.004838 2.004837
0.2 2.018731 2.018731

0.3 2.040818 2.040818
0.4 2.070320 2.070320

0.5 2.106531 2.106531
0.6 2.148812 2.148812

0.7 2.196586 2.196585
0.8 2.249329 2.249329

0.9 2.306570 2.306570
1.0 2.367880 2.367879

19.19. Method: RUNGE-KUTTA METHOD

Problem: y' = -y; y(0) = 1
ft = 0.1 True solution
x n
y n Y(x) = e-*
0.0 1.0000000 1.0000000

0.1 0.9048375 0.9048374

0.2 0.8187309 0.8187308
0.3 0.7408184 0.7408182
0.4 0.6703203 0.6703201

0.5 0.6065309 0.6065307

0.6 0.5488119 0.5488116
0.7 0.4965856 0.4965853
0.8 0.4493293 0.4493290

0.9 0.4065700 0.4065697

1.0 0.3678798 0.3678794