print('\n Find stable zero of f(x) = 1- (1+d)x^2 -e^{-x}\n')
from numpy import exp

dt = 1; T = 20; N = int(T/dt); m = N//20

for d in range(9):
	x = 1/(1+d) 
	print(' Iteration x = x +dt*f(x)  for dt=1, d =',d)
	for i in range(N): 
		x = x + dt * (1 -(1+d)*x*x -exp(-x))	#  x = x +dt*f(x) 
		if(i%m == 0): print('i,t,x ',i,i*dt,x)

print("And now Newton's method")
for d in range(9):
	x = 1/(1+d)
	print(" Iteration x = x -f(x)/f'(x)  for d =", d)
	for i in range(7):
		f = 1-(1+d)*x*x-exp(-x)  	#  f(x)
		f1 = -2*(1+d)*x+exp(-x)		#  f'(x)
		x = x - f/f1  			#  x = x - f(x)/f'(x)
		print('n,x ',i+1,x)