**Celestial Mechanics on a Graphing Calculator**

An illustration of the Runge-Kutta algorithm appliedto the differential equation y' = 2y witha step size of 1 and initial value y(0) = 1/4.The predicted value is a linear combination, withcoefficients - following the (blue) slope 1/2 line at
`(0,1/4)`. This gives`y = 3/4`. - following the (green) line with the slope (1) picked up by theblue line at
`x = 1/2`. This gives`y = 5/4`. - following the (orange) line with the slope (3/2) picked up by thegreen line at
`x = 1/2`. This gives`y = 7/4`. - following the (black) line with the slope (7/2) picked up by theorange line at
`x = 1`. This gives`y = 15/4`.
(1/24)(3+10+14+15) = 1.75.The same computational load would buy 4 iterations of Euler'smethod yielding 1.265. The exact value is |