The fourth-order approximation invented by Runge and Kutta can be surprisingly accurate, even with a ridiculously large step size. To see this, for Problem, use the given step size with the IVP
y' = t+y , y(0) = 0
(a) Compute for a single step the Euler approximation, the second-order Runge-Kutta approximation, and the fourth-order Runge-Kutta approximation.
(b) Add the three approximations in part (a) to the graph of the actual solution, as given in Fig 1.4.8 and describe what you se