用Python进行数值ODE求解

用Python进行数值ODE求解

import scipy.integrate as integrateimport matplotlib.pyplot as pltimport numpy as nppi = np.pisqrt = np.sqrtcos = np.cossin = np.sindef deriv_z(z, phi):    u, udot = z    return [udot, -u + sqrt(u)]phi = np.linspace(0, 7.0*pi, 2000)zinit = [1.49907, 0]z = integrate.odeint(deriv_z, zinit, phi)u, udot = z.T# plt.plot(phi, u)fig, ax = plt.subplots()ax.plot(1/u*cos(phi), 1/u*sin(phi))ax.set_aspect('equal')plt.grid(True)plt.show()