# Euler's method

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.

Select method:
Euler
Runge-Kutta order 2