import matplotlib . pyplot as plt
import numpy as np
t=0.1
x=0
y=1
x1=0
y1=1
xx=np.zeros(100)
yy=np.zeros(100)
xx1=np.zeros(100)
yy1=np.zeros(100)
for i in range(100):
y1=t*(y1-2*x1/y1)+y1
x1=x1+t
xx1[i]=x1
yy1[i]=y1
k=y-2*x/y
x=x+t
yn=y+t*(y-2*x/y)
k1=yn-2*x/yn
y=y+t*0.5*(k+k1)
xx[i]=x
yy[i]=y
print(xx[i],yy[i])
plt.plot(xx, yy, ls='-', lw=2, label='exact ola', color='red')
plt.plot(xx1, yy1, ls='-', lw=2, label='ola', color='pink')
plt.legend()
plt.show()
0.1 1.0947407407407408
0.2 1.1815989872420725
0.30000000000000004 1.262182136761762
0.4 1.3375855180594545
0.5 1.4085876084109334
0.6 1.4757566926132868
0.7 1.5395131494886805
0.7999999999999999 1.600167494015343
0.8999999999999999 1.6579441776071073
0.9999999999999999 1.7129964471279577
1.0999999999999999 1.7654151971804044
1.2 1.815233471391943
1.3 1.862427525447384
1.4000000000000001 1.9069148942879874
1.5000000000000002 1.9485495720419295
1.6000000000000003 1.9871141374299772
1.7000000000000004 2.0223083860198074
1.8000000000000005 2.053733716603174
1.9000000000000006 2.080872107298723
2.0000000000000004 2.1030579290503666
2.1000000000000005 2.119439951911353
2.2000000000000006 2.1289294777684855
2.3000000000000007 2.1301281628013062
2.400000000000001 2.121224949443421
2.500000000000001 2.099843889091529
2.600000000000001 2.062809649102652
2.700000000000001 2.0057657794721777
2.800000000000001 1.9225070235100412
2.9000000000000012 1.803692782992206
3.0000000000000013 1.6340039068834684
3.1000000000000014 1.3843817538947574
3.2000000000000015 0.9809612993403269
3.3000000000000016 -0.08820052857647642
3.4000000000000017 3.9848355059734004
3.5000000000000018 4.225954701119418
3.600000000000002 4.497949737177844
3.700000000000002 4.804618360471661
3.800000000000002 5.150066116313043
3.900000000000002 5.538730930710688
4.000000000000002 5.975414953730937
4.100000000000001 6.465324256380526
4.200000000000001 7.014116620810263
4.300000000000001 7.6279574118713445
4.4 8.313583395073652
4.5 9.07837436942535
4.6 9.930432589462766
4.699999999999999 10.87867012540282
4.799999999999999 11.932904520904371
4.899999999999999 13.103963328650407
4.999999999999998 14.403798318490262
5.099999999999998 15.845610353593342
5.1999999999999975 17.443986115988384
5.299999999999997 19.21504803723482
5.399999999999997 21.1766189581792
5.4999999999999964 23.348403209858162
5.599999999999996 25.752185981509864
5.699999999999996 28.412053026661265
5.799999999999995 31.354632959010885
5.899999999999995 34.609364610376275
5.999999999999995 38.208792166935595
6.099999999999994 42.18889107071666
6.199999999999994 46.589427974032226
6.299999999999994 51.45435836863142
6.399999999999993 56.83226588220475
6.499999999999993 62.77684764627669
6.5999999999999925 69.34745059552094
6.699999999999992 76.60966406362893
6.799999999999992 84.63597460001637
6.8999999999999915 93.50648955036928
6.999999999999991 103.30973662840964
7.099999999999991 114.143547463066
7.19999999999999 126.11603394196045
7.29999999999999 139.3466670970696
7.39999999999999 153.96746930077376
7.499999999999989 170.12433167044168
7.599999999999989 187.97846982845547
7.699999999999989 207.70803254459824
7.799999999999988 229.50987931275898
7.899999999999988 253.60154459915455
7.999999999999988 280.2234083615319
8.099999999999987 309.6410944966663
8.199999999999987 342.1481211474381
8.299999999999986 378.0688293135314
8.399999999999986 417.7616189864267
8.499999999999986 461.6225250975425
8.599999999999985 510.0891689587451
8.699999999999985 563.6451246207985
8.799999999999985 622.8247437150566
8.899999999999984 688.2184869181052
8.999999999999984 760.4788152337796
9.099999999999984 840.3266998724508
9.199999999999983 928.5588156794119
9.299999999999983 1026.0554898841913
9.399999999999983 1133.7894854787091
9.499999999999982 1252.8357068595728
9.599999999999982 1384.3819245715601
9.699999999999982 1529.7406261572748
9.799999999999981 1690.3621113535205
9.89999999999998 1867.8489622902418
9.99999999999998 2063.972033066781
