The red function is the mystery function. We'd like to know what the value of the function is when x = 1 but we only know its derivative and the value at x = 0, the black point. The blue line is the solution using Euler's method. The green line is the solution using the Runge-Kutta method. Click the mouse to zoom in.
The Runge-Kutta solution looks more choppy because I used a step size, or "h" of only 0.2 so it only took 5 steps. But it came closer to the actual value of 0.89 than the Euler method. I used an h of 0.025 for the Euler solution so it looks like it hugged the red curve more closely but it just took a ton more steps and didn't get as close as the RK approximation.