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Toyo ode.py update #10

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Toyo ode.py update #10

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e4eae5b
Update ode.py
toyofumi-yamauchi Sep 16, 2022
ad63ca5
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toyofumi-yamauchi Sep 16, 2022
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toyofumi-yamauchi Sep 16, 2022
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150 changes: 150 additions & 0 deletions ode/python/ode.py
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Original file line number Diff line number Diff line change
Expand Up @@ -259,3 +259,153 @@ def wray3( fun, x, y0 ):
y[n+1,:] = y[n,:] + 1.0*k1/4.0 + 0.0*k2 + 3.0*k3/4.0
return y

## HW2 Extra Credit
# Heun 2nd order
def heun( fun, x, y0):
'''
Explicit Heun 2nd order
-----------------------------
Butcher Table:

0 | 0 0
1 | 1 0
-----------------
| 1/2 1/2
'''
N = np.size( x )
h = x[1] - x[0]
I = np.size ( y0 )
y = np.zeros((N,I))
y[0,:] = y0
for n in range(0,N-1):
k1 = h * fun( x[n] , y[n,:])
k2 = h * fun( x[n] , y[n,:]+k1)
y[n+1,:] = y[n,:] + k1/2.0 + k2/2.0
return y

# Kutta 3rd order
def kutta( fun, x, y0):
'''
Explicit Kutta 3rd order
-----------------------------
Butcher Table:
0 | 0 0 0
1/2 | 1/2 0 0
1 |-1 2 0
---------------------
| 1/6 2/3 1/6
'''
N = np.size( x )
h = x[1] - x[0]
I = np.size ( y0 )
y = np.zeros((N,I))
y[0,:] = y0
for n in range(0,N-1):
k1 = h * fun( x[n] , y[n,:])
k2 = h * fun( x[n]+h/2 , y[n,:]+k1/2)
k3 = h * fun( x[n]+h , y[n,:]-k1+2*k2)
y[n+1,:] = y[n,:] + k1/6.0 + k2*2.0/3.0 + k3/6.0
return y

# Runge-Kuta 3/8-rule 4th order
def rk38( fun, x, y0 ):
'''
Runge-Kutta 3/8-rule 4th order
-----------------------------
Butcher Table:

0 | 0 0 0 0
1/3 | 1/3 0 0 0
2/3 |-1/3 1 0 0
1 | 1 -1 1 0
-----------------------------
| 1/8 3/8 3/8 1/8
'''
N = np.size( x )
h = x[1] - x[0]
I = np.size( y0 )
y = np.zeros((N,I))
y[0,:] = y0
for n in range(0, N-1):
k1 = h * fun( x[n] , y[n,:] )
k2 = h * fun( x[n]+h/3.0 , y[n,:]+k1/3.0 )
k3 = h * fun( x[n]+h*2/3.0 , y[n,:]-k1/3.0 + k2)
k4 = h * fun( x[n]+h , y[n,:]+k1 - k2)
y[n+1,:] = y[n,:] + k1/8.0 + k2*3.0/8.0 + k3*3.0/8.0 + k4/8.0
return y

# Ralston 4th order
def Ralston( fun, x, y0 ):
'''
Ralston 4th order
-----------------------------
Butcher Table:

0 | 0 0 0 0
0.4 | 0.4 0 0 0
0.45573725 | 0.29697761 0.15875964 0 0
1 | 0.21810040 -3.05096516 3.83286576 0
-----------------------------------------------------------
| 0.17476028 -0.55148066 1.20553560 0.17118478
'''
N = np.size( x )
h = x[1] - x[0]
I = np.size( y0 )
y = np.zeros((N,I))
y[0,:] = y0
for n in range(0, N-1):
k1 = h * fun( x[n] , y[n,:] )
k2 = h * fun( x[n]+0.4*h , y[n,:]+0.4*k1 )
k3 = h * fun( x[n]+0.45573725*h , y[n,:]+0.29697761*k1 + 0.15875964*k2 )
k4 = h * fun( x[n]+h , y[n,:]+0.21810040*k1 - 3.05096516*k2 + 3.83286576*k3 )
y[n+1,:] = y[n,:] + 0.17476028*k1 - 0.55148066*k2 + 1.20553560*k3 + 0.17118478*k4
return y

## HW3
# Runge-Kutta 4th for 2nd order ODE
def rk4_2nd(f, g, t, initial):
N = np.size( t )
h = t[1] - t[0]
I = np.size(initial)
xv = np.zeros((N,I))
xv[:,0] = initial[0]
xv[:,1] = initial[1]
for n in range(0, N-1):
k1 = h * f(t[n], xv[n,0], xv[n,1])
l1 = h * g(t[n], xv[n,0], xv[n,1])
k2 = h * f(t[n]+h/2.0, xv[n,0]+k1/2.0, xv[n,1]+l1/2.0)
l2 = h * g(t[n]+h/2.0, xv[n,0]+k1/2.0, xv[n,1]+l1/2.0)
k3 = h * f(t[n]+h/2.0, xv[n,0]+k2/2.0, xv[n,1]+l2/2.0)
l3 = h * g(t[n]+h/2.0, xv[n,0]+k2/2.0, xv[n,1]+l2/2.0)
k4 = h * f(t[n]+h , xv[n,0]+k3 , xv[n,1]+l3 )
l4 = h * g(t[n]+h , xv[n,0]+k3 , xv[n,1]+l3 )
#print(k1,l1,k2,l2,k3,l3,k4,l4)
xv[n+1,0] = xv[n,0] + k1/6.0 + k2/3.0 + k3/3.0 + k4/6.0
xv[n+1,1] = xv[n,1] + l1/6.0 + l2/3.0 + l3/3.0 + l4/6.0
return xv

# Harmonic Oscillator Leapfrog
def leapfrog_2nd(f,g,t,initial):
N = np.size( t )
h = t[1] - t[0]
I = np.size(initial)
xv = np.zeros((N,I))
xv[:,0] = initial[0]
xv[:,1] = initial[1]
for n in range(0, N-1):
xv[n+1,0] = (1-h**2/2) *xv[n,0] + (h) *xv[n,1]
xv[n+1,1] = (-h+h**3/4)*xv[n,0] + (1-h**2/2)*xv[n,1]
return xv

def leapfrog_2nd_f_correction(f,g,t,initial):
N = np.size( t )
h = t[1] - t[0]
I = np.size(initial)
xv = np.zeros((N,I))
xv[:,0] = initial[0]
xv[:,1] = initial[1]
Omega_new = np.sin(h/2)/(h/2)
for n in range(0, N-1):
xv[n+1,0] = (1-Omega_new**2*h**2/2) *xv[n,0] + (h) *xv[n,1]
xv[n+1,1] = (-Omega_new**2*h+Omega_new**4*h**3/4)*xv[n,0] + (1-Omega_new**2*h**2/2)*xv[n,1]
return xv