import matplotlib.pyplot as plt
from numpy import linspace, exp
from math import floor

la = -2.3
end_time = 5

exact_times = linspace(0, end_time, 100)
exact_solution = exp(la * exact_times)

euler1_h = 1;
euler1_N = int(floor(end_time / euler1_h))
euler1_times = [ k * euler1_h for k in range(euler1_N + 1) ]
euler1_solution = [ (1 + euler1_h * la) ** k for k in range(euler1_N + 1) ]

euler2_h = 0.7;
euler2_N = int(floor(end_time / euler2_h))
euler2_times = [ k*euler2_h for k in range(euler2_N + 1) ]
euler2_solution = [ (1 + euler2_h * la) ** k for k in range(euler2_N + 1) ]

plt.plot(exact_times, exact_solution, '-k',
         euler1_times, euler1_solution, ':sb',
         euler2_times, euler2_solution, ':or', markersize = 10)

plt.gca().tick_params(labelsize = 20)
plt.savefig('euler-instability.svg')