def test_one_step():
"""
test Euler and RK methods
"""
y0 = np.array([0., 1.])
t0 = 0
t1 = np.pi / 2
dt = 0.1
f = Harmonic(y0, 1, 1)
ts = np.arange(t0, t1 + dt, dt)
exact = f[ts].T
_, (ax1, ax2) = plt.subplots(1, 2)
ax1.plot(ts, [e[0] for e in exact], 'k', label='Exact')
colors = 'rgbcmyk'
for i, method in enumerate([
ExplicitEulerMethod(),
ImplicitEulerMethod(),
RungeKuttaMethod(collection.rk4_coeffs),
RungeKuttaMethod(collection.dopri_coeffs),
]):
f.clear_call_counter()
_, y = fix_step_integration(method, f, y0, ts)
n_calls = f.get_call_counter()
print(
f'One-step {method.name}: {len(y)-1} steps, {n_calls} function calls'
)
ax1.plot(ts, [_y[0] for _y in y], f'{colors[i]}.--', label=method.name)
ax2.plot(ts,
get_log_error(exact, y),
f'{colors[i]}.--',
label=method.name)
ax1.set_xlabel('t'), ax1.set_ylabel('y'), ax1.legend()
ax2.set_xlabel('t'), ax2.set_ylabel('accuracy'), ax2.legend()
plt.suptitle('test_one_step')
plt.show()
def test_multi_step():
"""
Проверяем методы Адамса
Q: сравните правые графики для обоих случаев и объясните разницу
"""
y0 = np.array([0., 1.])
t0 = 0
t1 = 1.
dt = 0.1
f = Harmonic(y0, 1, 1)
ts = np.arange(t0, t1+dt, dt)
exact = f[ts].T
for one_step_method in [
RungeKuttaMethod(collection.rk4_coeffs),
ExplicitEulerMethod(),
]:
_, (ax1, ax2) = plt.subplots(1, 2)
ax1.plot(ts, [e[0] for e in exact], 'k', label='Exact')
for p, c in adams_coeffs.items():
f.clear_call_counter()
t_adams, y_adams = adams(f, y0, ts, c,
one_step_method=one_step_method)
n_calls = f.get_call_counter()
print(f'{p}-order multi-step with one-step {one_step_method.name}: {n_calls} function calls')
err = get_accuracy(exact, y_adams)
label = f"Adams's order {p}"
ax1.plot(t_adams, [y[0] for y in y_adams], '.--', label=label)
ax2.plot(t_adams, err, '.--', label=label)
ax1.set_xlabel('t'), ax1.set_ylabel('y'), ax1.legend()
ax2.set_xlabel('t'), ax2.set_ylabel('accuracy'), ax2.legend()
plt.suptitle(f'test_multi_step\none step method: {one_step_method.name}')
plt.show()