Page 200 - Schaum's Outline of Differential Equations

CHAP. 19] NUMERICAL METHODS FOR SOLVING DIFFERENTIAL EQUATIONS 183

Continuing in this manner, we generate Table 19-4.

Table 19-4

Method: RUNGE-KUTTA METHOD

Problem: y' = y;y(Q)=l
ft = 0.1 True solution
x n
y n Y(x) = e x
0.0 1.0000000 1.0000000

0.1 1.1051708 1.1051709
0.2 1.2214026 1.2214028

0.3 1.3498585 1.3498588
0.4 1.4918242 1.4918247
0.5 1.6487206 1.6487213

0.6 1.8221180 1.8221188

0.7 2.0137516 2.0137527
0.8 2.2255396 2.2255409

0.9 2.4596014 2.4596031
1.0 2.7182797 2.7182818

2
19.6. Use the Runge-Kutta method to solve / = y + 1; y(0) = 0 on the interval [0,1] with h = 0.1.
Here/(X y) = y 2 + 1. Using Eq. (19.5) we compute