import numpy as np
from matplotlib import pyplot as plt 
%matplotlib inline

xmin = 0.0
xmax = 1.0
N    = 3

xgrid = np.linspace(xmin, xmax, N)
dx    = 1.0 * (xmax - xmin) / (N - 1.0)
f    = np.ones(N)

for i in range(1,N):
    f[i] = f[i-1] + dx * np.exp(xgrid[i-1])
    
ftrue = np.exp(xgrid)

plt.plot(xgrid, ftrue, 'r--', linewidth = 4, label = 'Actual Solution')
plt.plot(xgrid, f, 'b-', linewidth = 4, label = 'Approximate Solution')
plt.legend(loc = 'upper left')
plt.xlabel('x')
plt.ylabel('f(x)')
plt.title('Finite Difference Solution: N = 3')
plt.show()

xmin = 0.0
xmax = 1.0
N    = 30

xgrid = np.linspace(xmin, xmax, N)
dx    = 1.0 * (xmax - xmin) / (N - 1.0)
f    = np.ones(N)

for i in range(1,N):
    f[i] = f[i-1] + dx * np.exp(xgrid[i-1])
    
ftrue = np.exp(xgrid)

plt.plot(xgrid, ftrue, 'r--', linewidth = 4, label = 'Actual Solution')
plt.plot(xgrid, f, 'b-', linewidth = 4, label = 'Approximate Solution')
plt.legend(loc = 'upper left')
plt.xlabel('x')
plt.ylabel('f(x)')
plt.title('Finite Difference Solution: N = 30')
plt.show()