zout[:] = [z[1], g - alpha*z[1]**2]
return zout
# main program starts here
T = 10 # end of simulation
N = 20 # no of time steps
time = np.linspace(0, T, N+1)
z0=np.zeros(2)
z0[0] = 2.0
ze = euler(f, z0, time) # compute response with constant CD using Euler's method
ze2 = euler(f2, z0, time) # compute response with varying CD using Euler's method
zh = heun(f, z0, time) # compute response with constant CD using Heun's method
zh2 = heun(f2, z0, time) # compute response with varying CD using Heun's method
k1 = np.sqrt(g*4*rho_s*d/(3*rho_f*CD))
k2 = np.sqrt(3*rho_f*g*CD/(4*rho_s*d))
v_a = k1*np.tanh(k2*time) # compute response with constant CD using analytical solution
# plotting
legends=[]
line_type=['-',':','.','-.','--']
plot(time, v_a, line_type[0])
legends.append('Analytical (constant CD)')
plot(time, ze[:,1], line_type[1])
# main program starts here T = 10 # end of simulation N = 20 # no of time steps time = np.linspace(0, T, N + 1) z0 = np.zeros(2) z0[0] = 2.0 # compute response with constant CD using Euler's method ze = euler(f, z0, time) # compute response with varying CD using Euler's method ze2 = euler(f2, z0, time) # compute response with constant CD using Heun's method zh = heun(f, z0, time) # compute response with varying CD using Heun's method zh2 = heun(f2, z0, time) zrk4 = rk4(f, z0, time) # compute response with constant CD using RK4 zrk4_2 = rk4(f2, z0, time) # compute response with varying CD using RK4 k1 = np.sqrt(g * 4 * rho_s * d / (3 * rho_f * CD)) k2 = np.sqrt(3 * rho_f * g * CD / (4 * rho_s * d)) # compute response with constant CD using analytical solution v_a = k1 * np.tanh(k2 * time) # plotting legends = [] line_type = ['-', ':', '.', '-.', ':', '.', '-.']