Runge Kutta
Runge-Kutta techniques were developed by two German mathematicians C. Runge and M.W. Kutta. These techniques are important in the field of solving ordinary differential equations through explicit and implicit iterative methods.
y' = f(t,y) where y(t0) = y0
Then, the Runge-Kutta 4 method for this problem is:
yn+1 = yn + h*(k1 + 2*k2 + 2*k3 + k4)/6
tn+1 = tn + h
where yn+1 is the Runge-Kutta 4 approximation of y(tn+1) .
k1 = f(tn, yn)
k2 = f(tn + h/2, yn + h*k1/2)
k3 = f(tn + h/2, yn + h*k2/2)
k4 = f(tn + h, yn + h*k3)