#simple exponential potential
	# u = K*phi'/H0; v = omega_matter**(1/3)*(1+z); w = l*K*phi' - ln((K**2)*V0/H0**2)
	# f,g,h are functions of derivation of u,v,w respectively derieved w.r.t t*H0 = T

	import matplotlib.pyplot as plt
	import numpy as np
	import math

	def f(T,u,v,w):
    	return -3*u*((v**3 + (u**2)/6 + np.exp(-w)/3)**0.5) + l*np.exp(-w)

	def g(T,u,v,w):
		return -v*(v**3 + (u**2)/6 + np.exp(-w)/3)**0.5

	def h(T,u):
		return l*u

	p = 0.1
	q = 1.0
	dh = 0.1
	n = (q-p)/dh
	u = [0.0]
	v = [1100]
	T = [0.00001]
	w = [-44.927]
	l = 1.3

	for i in range(0,int(n)):
    	k1 = f(T[i],u[i],v[i],w[i])
    	r1 = g(T[i],u[i],v[i],w[i])
    	print k1, r1
    	s1 = h(T[i],u[i])
    	print s1
    	k2 = f(T[i] + 0.5*dh,u[i] + k1*dh,v[i] + k1*dh,w[i] + k1*dh)
    	r2 = g(T[i] + 0.5*dh,u[i] + r1*dh,v[i] + r1*dh,w[i] + r1*dh)
    	s2 = h(T[i] + 0.5*dh,u[i] + s1*dh)
    	print k2,r2,s2
    	k3 = f(T[i] + 0.5*dh,u[i] + k2*dh,v[i] + k2*dh,w[i] + k2*dh)
    	r3 = g(T[i] + 0.5*dh,u[i] + r2*dh,v[i] + r2*dh,w[i] + r2*dh)
    	s3 = h(T[i] + 0.5*dh,u[i] + s2*dh)
    	k4 = f(T[i] + dh,u[i] + dh*k3,v[i] + dh*k3,w[i] + k3*dh)
    	r4 = g(T[i] + dh,u[i] + r3*dh,v[i] + dh*r3,w[i] + r3*dh)
    	s4 = h(T[i] + dh,u[i] + dh*s3)
    	T == T.append(T[i] + dh)
    	u == u.append(u[i] + (dh/6)*(k1 + 2.0*k2 + 2.0*k3 + k4))
    	v == v.append(v[i] + (dh/6)*(r1 + 2.0*r2 + 2.0*r3 + r4))
    	w == w.append(w[i] + (dh/6)*(s1 + 2.0*s2 + 2.0*s3 + s4))

	plt.plot(T,u, '-b')
	plt.plot(T,v, '-r')
	plt.plot(T,w, '-g')
	plt.title('quintessence cosmological model')
	plt.show()