import numpy as np
import matplotlib.pyplot as plt
t=0.1
x=0
y=1
i=1
yy=np.zeros((100))
xx=np.zeros((100))
for i in range(100):
k=y-2*x/y
x=x+t
y1=y+t*k
k1=y1-2*x/y1
y=y+t*(k+k1)*0.5
xx[i]=x
yy[i]=y
print(x,y)
plt.plot(xx, yy)
plt.show()
0.1 1.095909090909091
0.2 1.1840965692429972
0.30000000000000004 1.2662013608757763
0.4 1.3433601514839986
0.5 1.4164019285369094
0.6 1.485955602415669
0.7 1.5525140913261455
0.7999999999999999 1.6164747827520576
0.8999999999999999 1.6781663636751858
0.9999999999999999 1.7378674010354138
1.0999999999999999 1.795819744910657
1.2 1.8522385990502925
1.3 1.9073204178377563
1.4000000000000001 1.9612493906319577
1.5000000000000002 2.0142030360599446
1.6000000000000003 2.066357283013655
1.7000000000000004 2.1178913249274696
1.8000000000000005 2.1689924782789043
1.9000000000000006 2.2198612426004756
2.0000000000000004 2.2707167397657666
2.1000000000000005 2.32180269966453
2.2000000000000006 2.373394153728064
2.3000000000000007 2.4258049938401265
2.400000000000001 2.479396548830104
2.500000000000001 2.5345873206656235
2.600000000000001 2.5918640039575958
2.700000000000001 2.651793881429891
2.800000000000001 2.715038640456334
2.9000000000000012 2.7823695879838817
3.0000000000000013 2.854684151012614
3.1000000000000014 2.933023438205294
3.2000000000000015 3.0185905110668165
3.3000000000000016 3.1127688834370595
3.4000000000000017 3.2171406572597903
3.5000000000000018 3.3335036404708074
3.600000000000002 3.4638868141440735
3.700000000000002 3.6105636532638243
3.800000000000002 3.776063077959879
3.900000000000002 3.9631782135250067
4.000000000000002 4.17497362733908
4.100000000000001 4.414792214087622
4.200000000000001 4.686263321770158
4.300000000000001 4.993313958871075
4.4 5.340184940330469
4.5 5.731453613913819
4.6 6.172064414060677
4.699999999999999 6.667368012258599
4.799999999999999 7.223169376499369
4.899999999999999 7.845784702735553
4.999999999999998 8.54210698550867
5.099999999999998 9.319679958975971
5.1999999999999975 10.186780237956588
5.299999999999997 11.152507679941843
5.399999999999997 12.226884230333251
5.4999999999999964 13.420961769562055
5.599999999999996 14.746939729248727
5.699999999999996 16.21829347387518
5.799999999999995 17.84991465230495
5.899999999999995 19.658264913448832
5.999999999999995 21.661544558967204
6.099999999999994 23.879877880615012
6.199999999999994 26.33551710791327
6.299999999999994 29.053067079707077
6.399999999999993 32.05973295633575
6.499999999999993 35.385593512244014
6.5999999999999925 39.06390279591596
6.699999999999992 43.13142321861966
6.799999999999992 47.628793439022616
6.8999999999999915 52.60093475067547
6.999999999999991 58.097500057198566
7.099999999999991 64.17336993952766
7.19999999999999 70.88920078491002
7.29999999999999 78.31203046304113
7.39999999999999 86.51594760583606
7.499999999999989 95.58283117943135
7.599999999999989 105.60316773632505
7.699999999999989 116.67695450897538
7.799999999999988 128.9146973613376
7.899999999999988 142.4385135601939
7.999999999999988 157.38335037310645
8.099999999999987 173.89833165478166
8.199999999999987 192.14824586006776
8.299999999999986 212.315190332423
8.399999999999986 234.60038827554476
8.499999999999986 259.22619653847477
8.599999999999985 286.438324248066
8.699999999999985 316.50828442619735
8.799999999999985 349.7361030535278
8.899999999999984 386.4533126100826
8.999999999999984 427.0262599611741
9.099999999999984 471.8597615934031
9.199999999999983 521.4011426710401
9.299999999999983 576.1447002125335
9.399999999999983 636.6366349184326
9.499999999999982 703.4805008578703
9.599999999999982 777.3432273875706
9.699999999999982 858.9617733866818
9.799999999999981 949.1504801995546
9.89999999999998 1048.8091966498191
9.99999999999998 1158.932257192333
