Using the improved Euler method with a step size of $h = 0.1$ , the solution of $y ^ { \prime } = 1 - y ^ { 2 } , y ( 0 ) = 0$ at $x = 0.1$ is
A) $y _ { 1 } = 0.095$
B) $y _ { 1 } = 0.995$
C) $y _ { 1 } = 0.95$
D) $y _ { 1 } = 0.00995$
E) $y _ { 1 } = 0.0995$

Question

Quizplus · Accepted Answer

The improved Euler method (Heun's method) involves calculating an intermediate slope and using it to find the next value. Here, the intermediate slope is calculated using the initial slope and the slope at the predicted point. The calculation gives $y_1 \approx 0.0995$.

Using the Improved Euler Method with a Step Size Of h