# Numerical solution of a differential equation
import numpy as np
import math
import matplotlib.pyplot as plt

dx=0.01
tau=0.5
x_end=10

N=int(x_end/dx)
Numerical_Solution=np.zeros(N)
x=np.zeros(N)
Analytic_Solution=np.zeros(N)

Numerical_Solution[0]=1
x[0]=0
Analytic_Solution[0]=1

for i in range (1,N):
    Numerical_Solution[i]=Numerical_Solution[i-1]+dx*(tau)*Numerical_Solution[i-1]
    x[i]=x[i-1]+dx
    Analytic_Solution[i]=math.exp(tau*x[i])


fig = plt.figure(figsize=(8,4))
# --- left hand plot
ax = fig.add_subplot(1,3,1)
plt.plot(x,Numerical_Solution,color='red')
#ax.legend(loc='best')
plt.title('Numerical Solution')

# --- right hand plot
ax = fig.add_subplot(1,3,2)
plt.plot(x,Analytic_Solution,color='blue')
plt.title('Analytic Solution')

#ax.legend(loc='best')
ax = fig.add_subplot(1,3,3)
plt.plot(x,Analytic_Solution-Numerical_Solution,color='blue')
plt.title('Error')

# --- title, explanatory text and save
fig.suptitle('Exponential Growth Solution', fontsize=20)
plt.tight_layout()
plt.subplots_adjust(top=0.85)