def P45():
def initCond(u):
return np.array([0.0, u])
def r(u):
X, Y = hw7.integrate(F, xStart, initCond(u), xStop, h, tol=tol)
y = Y[len(Y) - 1]
r = y[0] - 1.0
return r
def F(x, y):
F = np.zeros(2) #Y=[y,y',y'']
F[0] = y[1]
F[1] = -1 * (1 - 0.2 * x) * (y[0]**2)
return F
xStart = 0.0
xStop = pi / 2
u1 = 0.77
u2 = 0.8
h = 0.01
tol = 1e-3
u = ridder(r, u1, u2)
print(u)
X, Y = hw7.integrate(F, xStart, initCond(u), xStop, h, tol=tol)
graph(X, Y, "P45")
def P46():
def initCond(u):
return np.array([0.0, u])
def r(u):
X, Y = hw7.integrate(F, xStart, initCond(u), xStop, h, tol=tol)
y = Y[len(Y) - 1]
r = y[0] - -1.0
return r
def F(x, y):
F = np.zeros(2) #Y=[y,y',y'']
F[0] = y[1]
F[1] = -2 * y[1] - 3 * y[0]**2
return F
xStart = 0.0
xStop = 2
u1 = -1.0
u2 = -0.95
h = 0.01
tol = 1e-3
u = ridder(r, u1, u2)
print(u)
X, Y = hw7.integrate(F, xStart, initCond(u), xStop, h, tol=tol)
graph(X, Y, "P46")
def P47():
def initCond(u):
return np.array([1.0, u])
def r(u):
X, Y = hw7.integrate(F, xStart, initCond(u), xStop, h, tol=tol)
y = Y[len(Y) - 1]
r = y[0] - 0.0
return r
def F(x, y):
F = np.zeros(2) #Y=[y,y']
F[0] = y[1]
F[1] = (1 - np.exp(-1 * x)) * y[0]
return F
xStart = 0.0
xStop = 15.0
u1 = -0.5
u2 = -0.6
h = 0.001
tol = 1e-6
#u = ridder(r,u1,u2,tol=tol)
u = -0.61
print(u)
X, Y = hw7.integrate(F, xStart, initCond(u), xStop, h, tol=tol)
graph(X, Y, "P47")
def r(u):
X, Y = hw7.integrate(F, xStart, initCond(u), xStop, h, tol=tol)
y = Y[len(Y) - 1]
r = y[0] - -1.0
return r