from math import exp

def cn_test(a,T,r0,n):
    """ Comparing explicit, implicit and Crank-Nicolson schemes, 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]
    
    re=r0 # explicit approximation
    ri=r0 # implicit approximation
    rcn=r0 # Crank-Nicolson approximation

    print '\n \t ex_error', '\t im_error', '\t cn_error'
    for k in range(n+1):
        error_e=abs(true_solution[k]-re)
        error_i=abs(true_solution[k]-ri)
        error_cn=abs(true_solution[k]-rcn)
        print '\t %f \t %f \t %f' % (error_e,error_i,error_cn)
       
        re=re+dt*a*re
        ri=ri/(1-dt*a)
        rcn=(rcn+dt/2*a*rcn)/(1-dt/2*a)