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()