def r(u): # Boundary condition residuals--see Eq. (8.7)
r = zeros(len(u), type=Float64)
X, Y = bulStoer(F, xStart, initCond(u), xStop, H)
y = Y[len(Y) - 1]
r[0] = y[0]
r[1] = y[2]
return r
def r(u): # Boundary condition residuals--see Eq. (8.7)
r = zeros(len(u),type=Float64)
X,Y = bulStoer(F,xStart,initCond(u),xStop,H)
y = Y[len(Y) - 1]
r[0] = y[0]
r[1] = y[2]
return r
return array([0.0, u[0], 0.0, u[1]])
def r(u): # Boundary condition residuals--see Eq. (8.7)
r = zeros(len(u), type=Float64)
X, Y = bulStoer(F, xStart, initCond(u), xStop, H)
y = Y[len(Y) - 1]
r[0] = y[0]
r[1] = y[2]
return r
def F(x, y): # First-order differential equations
F = zeros((4), type=Float64)
F[0] = y[1]
F[1] = y[2]
F[2] = y[3]
F[3] = x
return F
xStart = 0.0 # Start of integration
xStop = 1.0 # End of integration
u = array([0.0, 1.0]) # Initial guess for {u}
H = 0.5 # Printout incremant
freq = 1 # Printout frequency
u = newtonRaphson2(r, u, 1.0e-4)
X, Y = bulStoer(F, xStart, initCond(u), xStop, H)
printSoln(X, Y, freq)
raw_input("\nPress return to exit")
#!/usr/bin/python
## example7_11
from bulStoer import *
import numpy as np
import matplotlib.pyplot as plt
def F(x, y):
F = np.zeros(2)
F[0] = y[1]
F[1] = (-y[1] - y[0] / 0.45 + 9.0) / 2.0
return F
H = 0.25
xStop = 10.0
x = 0.0
y = np.array([0.0, 0.0])
X, Y = bulStoer(F, x, y, xStop, H)
plt.plot(X, Y[:, 1], '-o')
plt.xlabel('Time (s)')
plt.ylabel('Current (A)')
plt.grid(True)
plt.show()
input("\nPress return to exit")
def initCond(u): # Initial values of [y,y',y",y"'];
# use 'u' if unknown
return array([0.0, u[0], 0.0, u[1]])
def r(u): # Boundary condition residuals--see Eq. (8.7)
r = zeros(len(u),type=Float64)
X,Y = bulStoer(F,xStart,initCond(u),xStop,H)
y = Y[len(Y) - 1]
r[0] = y[0]
r[1] = y[2]
return r
def F(x,y): # First-order differential equations
F = zeros((4),type=Float64)
F[0] = y[1]
F[1] = y[2]
F[2] = y[3]
F[3] = x
return F
xStart = 0.0 # Start of integration
xStop = 1.0 # End of integration
u = array([0.0, 1.0]) # Initial guess for {u}
H = 0.5 # Printout incremant
freq = 1 # Printout frequency
u = newtonRaphson2(r,u,1.0e-4)
X,Y = bulStoer(F,xStart,initCond(u),xStop,H)
printSoln(X,Y,freq)
raw_input("\nPress return to exit")
## example7_11
from bulStoer import *
from numarray import array,zeros,Float64
from printSoln import *
def F(x,y):
F = zeros((2),type=Float64)
F[0] = y[1]
F[1] =(-y[1] - y[0]/0.45 + 9.0)/2.0
return F
H = 0.5
xStop = 10.0
x = 0.0
y = array([0.0, 0.0])
X,Y = bulStoer(F,x,y,xStop,H)
printSoln(X,Y,1)
raw_input("\nPress return to exit")
