"""
Ex. E.3 from "A primer on..." Solve the
same ODE as in E.1 and E.2, but now using
the ForwardEuler subclass from the ODESolver hierarchy.
The usage of this class is identical to the class used in E.2,
despite the different implementation, so most of the code is identical 
to ex E.2. 
"""

import numpy as np
import matplotlib.pyplot as plt
from ODESolver import ForwardEuler


class RHS:
    def __init__(self, r):
        self.r = r

    def __call__(self, t, u):
        return self.r * u


problem = RHS(0.1)
solver = ForwardEuler(problem)
solver.set_initial_condition(u0 = 0.2)
T = 20
N = 4

t, u = solver.solve((0,T), N)
plt.plot(t, u, label=f'$\Delta t = $ {T/N}')
t_fine = np.linspace(0, T, 200)
plt.plot(t_fine, 0.2 * np.exp(0.1 * t_fine), label = 'Exact')
plt.legend()
plt.show()







plt.plot(t, u, label = f'dt={T / N}')
t_fine = np.linspace(0,T, 200)
plt.plot(t_fine, 0.2 * np.exp(0.1 * t_fine),label = 'exact')
plt.legend()
plt.show()