import numpy as np
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def f(t,y):
return (-y**2)
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def yip1(yi,h):
delta=1+4*h*yi
return((-1+sqrt(delta))/(2*h))
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def Euler (a,b,N,y0):
h=(b-a)/N
y=np.empty(N+1)
y[0]=y0
for i in range (N) :
t=a+i*h
y[i+1]=yip1 (y[i],h) # Euler implicite
# y[i+1]=y[i]+h*f(t,y[i]) # Euler explicite
return (y)
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m=Euler(0,5,50,1)
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m
array([ 1. , 0.91607978, 0.84472393, 0.78335883, 0.73006006,
0.68336173, 0.64212879, 0.60546947, 0.57267392, 0.5431705 ,
0.51649391, 0.49226175, 0.47015699, 0.44991467, 0.43131169,
0.41415893, 0.39829503, 0.38358155, 0.36989902, 0.35714385,
0.34522577, 0.33406577, 0.32359444, 0.3137505 , 0.30447971,
0.29573386, 0.28746996, 0.27964957, 0.27223821, 0.26520485,
0.25852151, 0.2521629 , 0.24610608, 0.24033022, 0.23481634,
0.22954716, 0.22450682, 0.21968086, 0.21505595, 0.21061988,
0.20636137, 0.20227006, 0.19833633, 0.19455131, 0.19090677,
0.18739508, 0.18400914, 0.18074236, 0.17758859, 0.17454209,
0.17159752])
array([ 1. , 0.91607978, 0.84472393, 0.78335883, 0.73006006,
0.68336173, 0.64212879, 0.60546947, 0.57267392, 0.5431705 ,
0.51649391, 0.49226175, 0.47015699, 0.44991467, 0.43131169,
0.41415893, 0.39829503, 0.38358155, 0.36989902, 0.35714385,
0.34522577, 0.33406577, 0.32359444, 0.3137505 , 0.30447971,
0.29573386, 0.28746996, 0.27964957, 0.27223821, 0.26520485,
0.25852151, 0.2521629 , 0.24610608, 0.24033022, 0.23481634,
0.22954716, 0.22450682, 0.21968086, 0.21505595, 0.21061988,
0.20636137, 0.20227006, 0.19833633, 0.19455131, 0.19090677,
0.18739508, 0.18400914, 0.18074236, 0.17758859, 0.17454209,
0.17159752])
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list_plot(list(m))
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