[2021 Fall] Final Exam - Question 2¶

Course: AP3021

In [1]:

from scipy import integrate
from scipy.special import erf
import numpy as np

from scipy import integrate from scipy.special import erf import numpy as np

In [2]:

def q(z):
    qz = -6.01 * (z**8) + 4.92 * (z**7) - 0.024 * (z**4) + 0.13 * (z**3) - 0.37 * (z**2) - 1.88 * z + 20.00
    return qz

def q(z): qz = -6.01 * (z**8) + 4.92 * (z**7) - 0.024 * (z**4) + 0.13 * (z**3) - 0.37 * (z**2) - 1.88 * z + 20.00 return qz

In [3]:

Pw = 1000 * 1000 * 1000 * 1000
g = 9.8 * 0.001
para = 1 / (Pw * g)

x = np.array([
    0.,1.,2.,
    3., 4., 5., 
    6., 7., 8., 
    9., 10.]
)
# x = np.array([0.,1000.,2000.,3000., 4000., 5000., 6000., 7000., 8000., 9000., 10000.])
fx = q(x)
trap = np.trapz(fx, dx=1)
simp = integrate.simps(fx,dx=1)
romb = integrate.romberg(q, 0, 10)
quad = float((integrate.quadrature(q, 0.0, 10.0))[0])

Pw = 1000 * 1000 * 1000 * 1000 g = 9.8 * 0.001 para = 1 / (Pw * g) x = np.array([ 0.,1.,2., 3., 4., 5., 6., 7., 8., 9., 10.] ) # x = np.array([0.,1000.,2000.,3000., 4000., 5000., 6000., 7000., 8000., 9000., 10000.]) fx = q(x) trap = np.trapz(fx, dx=1) simp = integrate.simps(fx,dx=1) romb = integrate.romberg(q, 0, 10) quad = float((integrate.quadrature(q, 0.0, 10.0))[0])

(a)

In [4]:

print('Trapezoid:', para * trap, '\nSimpson 1/3:', para * simp, '\nRomberg:', para * romb)

print('Trapezoid:', para * trap, '\nSimpson 1/3:', para * simp, '\nRomberg:', para * romb)

Trapezoid: -0.06563365285938773 
Simpson 1/3: -0.061971091222312896 
Romberg: -0.06186509695011337

(b)

In [5]:

print('Gauss-quadrature:', para * quad)

print('Gauss-quadrature:', para * quad)

Gauss-quadrature: -0.061865096950113295

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Last update: 2024-04-27