from math import exp

def ex_growth(a,T,r0,n):
    """ Explicit scheme, using n time intervals, for 
        r'(t)=a r(t) for 0<t<T 
        r(0) = r0 """

    dt=float(T)/n

    # Compute exact solution r(t)=r0 exp(at) 
    times=[i*dt for i in range(n+1)]
    true_solution=[r0*exp(a*t) for t in times]
    
    r=r0
    print '\n \t approximation', '\t error'
    for k in range(n+1):
        error=abs(true_solution[k]-r)
        print '\t %f \t %f' % (r,error)
        r=r+dt*a*r