This is a demonstration of the effect of halving, or doubling, the step size for approximating solutions
to the intial problem
\[\frac{dx}{dt} = 0.05x, \hspace{5pt} x(0) = 100,\]
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, \(x = 100e^{0.05t}\), in blue.