# Exponential ODE with Euler's method

import numpy as np
import matplotlib.pyplot as plt

k = 1.3
tfinal = 10
dt = 1.0
steps = int(tfinal / dt)
N = np.zeros(steps+1)
t = np.zeros(steps+1)
N[0] = 2.0
t[0] = 0.0
for i in range(steps):
    dN = k * N[i] * dt
    N[i+1] = N[i] + dN
    t[i+1] = t[i] + dt

# Display data
for i in range(steps+1):
    print( f"{t[i]:.1f} \t {N[i]:.2f}")


# plot results
plt.plot(t,N)
plt.xlabel('Time')
plt.ylabel('N')
plt.show()
"""
# Save results to a file
np.savetxt('ExpODEEulers.txt', np.transpose([t,N]),
           fmt='%4.1f, %8.4f', newline='\n')
"""