def test_one_step():
"""
Проверяем методы Эйлера и Рунге-Кутты
"""
y0 = np.array([0., 1.])
t0 = 0
t1 = np.pi
ode = Harmonic(y0, 1, 1)
for dt in [0.1, 0.01]:
ts = np.arange(t0, t1 + dt, dt)
exact = ode[ts].T
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 4))
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),
]):
ode.clear_call_counter()
_, y = fix_step_integration(method, ode, y0, ts)
n_calls = ode.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_accuracy(exact, y),
f'{colors[i]}.--',
label=method.name)
ax1.legend(), ax1.set_title('y(t)')
ax2.legend(), ax2.set_title('accuracy')
fig.suptitle(f'test_one_step, dt={dt}')
fig.tight_layout()
plt.show()
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_accuracy(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_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
plt.figure()
plt.subplot(1, 2, 1)
plt.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),
]):
_, y = fix_step_integration(method, f, y0, ts)
print(f'len(Y): {len(y)}')
print(f'Function calls: {f.get_call_counter()}')
plt.subplot(1, 2, 1), plt.plot(ts, [_y[0] for _y in y],
f'{colors[i]}.--',
label=method.name)
plt.subplot(1, 2, 2), plt.plot(ts,
get_log_error(exact, y),
f'{colors[i]}.--',
label=method.name)
plt.subplot(1, 2, 1), plt.xlabel('t'), plt.ylabel('y'), plt.legend()
plt.subplot(1, 2, 2), plt.xlabel('t'), plt.ylabel('accuracy'), plt.legend()
plt.suptitle('test_one_step')
plt.show()