In [4]:

    

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


    

In [6]:

    

tmax = 10.0
M = 100
t = np.linspace(0, tmax, M)
t


    

    
Out[6]:





array([  0.        ,   0.1010101 ,   0.2020202 ,   0.3030303 ,
         0.4040404 ,   0.50505051,   0.60606061,   0.70707071,
         0.80808081,   0.90909091,   1.01010101,   1.11111111,
         1.21212121,   1.31313131,   1.41414141,   1.51515152,
         1.61616162,   1.71717172,   1.81818182,   1.91919192,
         2.02020202,   2.12121212,   2.22222222,   2.32323232,
         2.42424242,   2.52525253,   2.62626263,   2.72727273,
         2.82828283,   2.92929293,   3.03030303,   3.13131313,
         3.23232323,   3.33333333,   3.43434343,   3.53535354,
         3.63636364,   3.73737374,   3.83838384,   3.93939394,
         4.04040404,   4.14141414,   4.24242424,   4.34343434,
         4.44444444,   4.54545455,   4.64646465,   4.74747475,
         4.84848485,   4.94949495,   5.05050505,   5.15151515,
         5.25252525,   5.35353535,   5.45454545,   5.55555556,
         5.65656566,   5.75757576,   5.85858586,   5.95959596,
         6.06060606,   6.16161616,   6.26262626,   6.36363636,
         6.46464646,   6.56565657,   6.66666667,   6.76767677,
         6.86868687,   6.96969697,   7.07070707,   7.17171717,
         7.27272727,   7.37373737,   7.47474747,   7.57575758,
         7.67676768,   7.77777778,   7.87878788,   7.97979798,
         8.08080808,   8.18181818,   8.28282828,   8.38383838,
         8.48484848,   8.58585859,   8.68686869,   8.78787879,
         8.88888889,   8.98989899,   9.09090909,   9.19191919,
         9.29292929,   9.39393939,   9.49494949,   9.5959596 ,
         9.6969697 ,   9.7979798 ,   9.8989899 ,  10.        ])

In [3]:

    

h = t[1]-t[0]
print('h =', h)


    

    




h = 0.10101010101

In [4]:

    

N = 2
y = np.zeros((M,N))
print('N =', N)
print('M =', M)
print('y.shape =', y.shape)


    

    




N = 2
M = 100
y.shape = (100, 2)

In [1]:

    

from scipy.integrate import odeint


    

In [7]:

    

def solve_euler(derivs, y0, x):
    y = np.empty_like(x)
    y[0]= y0
    h = x[1] - x[0]
    for n in range(0, len(x)-1):
        y[n+1] = y[n] +h*derivs(y[n], x[n])
    return y


    

In [11]:

    

x = np.linspace(0, 1.0, 11)
y = np.empty_like(x)
y0 = y[0]
def derivs(y, x):
    return x+2*y
plt.plot(solve_euler(derivs, y0, x), color='orange')


    

    
Out[11]:





[<matplotlib.lines.Line2D at 0x7f3c29569710>]






    

In [ ]: