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In [5]:

    
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

l = 4
N = 100
x = np.linspace(-l/2,l/2,N)
y = np.linspace(-l/2,l/2,N)
X,Y = np.meshgrid(x,y)



In [6]:

    
dt =1e-4
Niter=1000
D=1
t = Niter*dt
P = 1/(4*np.pi*D*t)*np.exp(-(X**2+Y**2)/(4*D*t) )



In [8]:

    
plt.imshow(P)









    Out[8]:





<matplotlib.image.AxesImage at 0x7f8ef7fc16d0>



In [10]:

    
plt.plot( X[50,:],P[50,:])









    Out[10]:





[<matplotlib.lines.Line2D at 0x7f8ef56f3050>]



In [13]:

    
u = np.zeros((N,N))
dx = l/ (N-1.)
u[N//2, N//2 ]= 1.0/dx**2
C = D*dt/ (dx**2)
print C



In [14]:

    
for i in range(Niter):
    u[1:-1,1:-1] = u[1:-1,1:-1] +\
      C*(u[1:-1,:-2]+ u[1:-1,2:]+ u[:-2, 1:-1]+ u[2:,1:-1] -\
      4*u[1:-1,1:-1])



In [15]:

    
plt.imshow(u)









    Out[15]:





<matplotlib.image.AxesImage at 0x7f8ef5382b90>



In [ ]:

Zadanie 1

Zaimplementować ten sam algorytm z np.diff(..., axis=...)



In [13]:









    Out[13]: