# Exponential growth model solve.ivp
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import solve_ivp

# n - population size
def ExponentialModel(t, n):
    r = 1.2
    return r*n

n0 = 2.0
t0 = 0
tf = 10
steps = 1*tf
sol = solve_ivp(ExponentialModel, [t0, tf], [n0], method='RK45',
                rtol=1e-6, atol=1e-9, dense_output=True)
t = np.linspace(t0,tf,steps+1)
n = sol.sol(t)

# Display data
for i in range(steps+1):
    print( f"{t[i]:.1f} \t {n[0][i]:.4f}")

# plot results
plt.plot(t, n[0])
plt.xlabel('Time')
plt.ylabel('Population size')
plt.savefig('ExpSolveIVP.svg')

# Save results to a file
f = open('ExpODE_SolveIVP.txt', "w")
for i in range(0, steps+1, 1):
    print("%5.1f, %6.4f" % (t[i], n[0][i]), file=f)
f.close()