This is a demonstration of the effect of halving, or doubling, the step size for approximating solutions
to the intial problem
dxdt=0.05x,x(0)=100,
with either Euler's method or Runge-Kutta of order 2 (also know as the improved Euler's method). The approximate solution
is shown in red with the exact solution, x=100e0.05t, in blue.