Use the Explicit Modified Euler method to calculate x(h) if h = 0.2, x(0) = 1, and x(t) = (-x^2)(t) - 1.
The single hat is used to denote the first estimate of a x value and a double hat is used to denote a 2nd estimate .
The solution to and ODE in the form of x(t) = f(x,t)
is given by,
x_(k+1) = x_k + hf[t_k + h/2, x_k + h/2*f(t_k, x_k)]
where h is the time step and time advances according to tk+1 = tk + h.