In [5]:
# Importamos la libreria NumPy
import numpy as np
# Valores:
L = 500.0
g = 9.8
Aca = 20.0
Atu = 1.0
H = 100.0
h = 90.0
c = 0.01
q = 1.0
def f1(x,y1,y2):
return (1/Aca)*(Atu*y2 - q)
def f2(x,y1,y2):
return (g/L)*(H - y1 -c*y2**2)
def Derivs(n ,x ,y ,f1 ,f2):
dy = np.zeros(n)
dy[0] = f1(x,y[0],y[1])
dy[1] = f2(x,y[0],y[1])
return dy
def RK4(x,y,n,h,f1,f2):
ym = np.zeros(n)
ye = np.zeros(n)
slope = np.zeros(n)
k1 = np.zeros(n)
k2 = np.zeros(n)
k3 = np.zeros(n)
k4 = np.zeros(n)
k1 = Derivs(n ,x ,y ,f1 ,f2)
for ii in range(0,n):
ym[ii] = y[ii] + k1[ii]*(h/2)
k2 = Derivs(n ,x + h/2 ,ym ,f1 ,f2)
for ii in range(0,n):
ym[ii] = y[ii] + k2[ii]*(h/2)
k3 = Derivs(n ,x + h/2 ,ym ,f1 ,f2)
for ii in range(0,n):
ye[ii] = y[ii] + k3[ii]*h
k4 = Derivs(n ,x + h ,ye ,f1 ,f2)
for ii in range(0,n):
slope[ii] = (k1[ii] + 2 * (k2[ii] + k3[ii] ) + k4[ii])/6
y[ii] = y[ii] + slope[ii]*h
x = x + h
return x, y
def integrator(x,y,n,h,xend,f1,f2):
while (x < xend):
if (xend - x < h ):
h = xend - x
[x, y] = RK4(x,y,n,h,f1,f2)
return x, y
#*********************************
n = 2 # número de ecuaciones
y0 = np.zeros(n) # Valores inciales de 2 variables dependientes
xp = np.zeros([1,10000000])
y = np.zeros(n)
m = 1
yp = np.zeros([n,10000000])
y0 = [90,0.5]
xi = 0. # valor inicial de la variable independiente
xf = 400. # valor final de la variable independiente
dx = 0.5 # tamaño de paso
x = xi
m = 0
xp[0,m] = x
#yp = np.zeros([n,1])
for i in range(0,2):
m = 0
yp[i,m] = y0[i]
y[i] = y0[i]
#yp = np.zeros([n,100])
for i in range(0,2):
m = 0
yp[i,m] = y0[i]
y[i] = y0[i]
while x < xf:
xend = x + dx
if xend > xf:
xend = xf
h = dx
[x,y] = integrator(x,y,n,h,xend,f1,f2)
m = m + 1
xp[0,m] = x
for j in range(n):
yp[j,m] = y[j]
for ii in range(m+1):
print("%4.1f %10.6f %+12.6e" % (xp[0,ii], yp[0,ii], yp[1,ii]))
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
plt.subplot(2, 1, 1)
plt.plot(xp[0,0:m+1], yp[0,0:m+1],'b')
plt.title('Variables Hidraulicas')
plt.ylabel('Carga h(t) ')
plt.subplot(2, 1, 2)
plt.plot(xp[0,0:m+1], yp[1,0:m+1],'r')
plt.xlabel('tiempo (s)')
plt.ylabel('velocidad u(t) ')
plt.show()
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In [ ]:
Content source: alexander14rc/Programas
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