Runge Kutta de Cuarto Orden

7/24/2019 Runge Kutta de Cuarto Orden

1/15

LEYVER ANDRES AREVALO PERILLA 12471

x 0

y 1h 0.5

i x y k1

k2

x y

0 0 1 8.5 0.25 3.125

1 0.5 3.21875 1.25 0.75 3.53125

2 1 3 -1.5 1.25 2.625

3 1.5 2.21875 -1.25 1.75 1.90625

4 2 2 0.5 2.25 2.125

5 2.5 2.71875 2.25 2.75 3.28125

6 3 4 2.5 3.25 4.6257 3.5 4.71875 -0.25 3.75 4.65625

8 4 3 -7.5 4.25 1.125

9 4.5 -3.78125 -20.75 4.75 -8.96875

10 5 -19 -41.5 5.25 -29.375

0 1 2

-25

-20

-15

-10

-5

0

5

10


2/15

k3 k4

k2 x y k3 x y

4.21875 0.25 2.0546875 4.21875 0.5 3.109375

-0.59375 0.75 3.0703125 -0.59375 1 2.921875

-1.65625 1.25 2.5859375 -1.65625 1.5 2.171875

-0.46875 1.75 2.1015625 -0.46875 2 1.984375

1.46875 2.25 2.3671875 1.46875 2.5 2.734375

2.65625 2.75 3.3828125 2.65625 3 4.046875

1.59375 3.25 4.3984375 1.59375 3.5 4.796875-3.21875 3.75 3.9140625 -3.21875 4 3.109375

-13.28125 4.25 -0.3203125 -13.28125 4.5 -3.640625

-30.09375 4.75 -11.3046875 -30.09375 5 -18.828125

-55.15625 5.25 -32.7890625 -55.15625 5.5 -46.578125

3 4 5


3/15

yi +1k4

1.25 3.21875

-1.5 3

-1.25 2.21875

0.5 2

2.25 2.71875

2.5 4

-0.25 4.71875-7.5 3

-20.75 -3.78125

-41.5 -19

-71.25 -46.78125

6

Col!" D


4/15

x 0

y 2h 0.5

i x y k1

k2

x y

0 0 2 3 0.25 2.75

1 0.5 3.7516995 4.09144904 0.75 4.77456176

2 1 6.19504199 5.80464272 1.25 7.64620267

3 1.5 9.70777193 8.42658173 1.75 11.8144174

4 2 14.845106 12.3895767 2.25 17.9425002

5 2.5 22.428857 18.3417959 2.75 27.014306

6 3 33.6799839 27.2527136 3.25 40.49316237 3.5 50.4160172 40.5705785 3.75 60.5586618

8 4 75.3453361 60.4574528 4.25 90.4596993

9 4.5 112.505986 90.1399449 4.75 135.040972

10 5 167.920167 134.432516 5.25 201.528297

0 1 2

0

20

40

60

80

100

120

140

160

180


5/15

k3 k4

k2 x y k3 x y

3.51061103 0.25 2.87765276 3.44678465 0.5 3.72339233

4.90119432 0.75 4.97699808 4.79997616 1 6.15168758

7.05002598 1.25 7.95754849 6.89435307 1.5 9.64221853

10.3135912 1.75 12.2861697 10.077715 2 14.7466294

15.2273398 2.25 18.651941 14.8726194 2.5 22.2814157

22.592901 2.75 28.0770822 22.0615129 3 33.4596134

33.608371 3.25 42.0820766 32.8139138 3.5 50.086940850.0628168 3.75 62.9317214 48.876287 4 74.8541607

74.6265506 4.25 94.0019737 72.8554133 4.5 111.773043

111.284252 4.75 140.327049 108.641214 5 166.826593

165.981176 5.25 209.415461 162.037593 5.5 248.938964

3 4 5


6/15

yi +1k4

4.10560263 3.7516995

5.82631992 6.19504199

8.45935843 9.70777193

12.438815 14.845106

18.4155165 22.428857

27.3628988 33.6799839

40.7351167 50.416017260.7030404 75.3453361

90.5064164 112.505986

134.979304 167.920167

201.333993 250.570505

6

Col!" D


7/15

x 0

y0 4h 0.5

i x y k1

k2

x y

0 0 4 -2 0.25 3.5

1 0.5 3.11523438 -1.55761719 0.75 2.72583008

2 1 2.4261713 -1.21308565 1.25 2.12289989

3 1.5 1.88952306 -0.94476153 1.75 1.65333268

4 2 1.4715768 -0.7357884 2.25 1.2876297

5 2.5 1.14607666 -0.57303833 2.75 1.00281707

6 3 0.89257435 -0.44628717 3.25 0.781002567 3.5 0.69514457 -0.34757229 3.75 0.6082515

8 4 0.54138457 -0.27069228 4.25 0.4737115

9 4.5 0.42163495 -0.21081748 4.75 0.36893058

10 5 0.32837293 -0.16418646 5.25 0.28732631

x 0

y0 6

h 0.5

i x y k1k2

x y

0 0 6 1.8 0.25 6.45

1 0.5 6.85767031 1.63117547 0.75 7.26546418

2 1 7.63210567 1.46775117 1.25 7.99904347

3 1.5 8.32688598 1.3129819 1.75 8.65513145

4 2 8.9468651 1.16878279 2.25 9.2390608

5 2.5 9.49760136 1.03611193 2.75 9.75662934

6 3 9.98495402 0.91525636 3.25 10.2137681

7 3.5 10.4148036 0.80604447 3.75 10.6163147

8 4 10.7928635 0.70800249 4.25 10.9698641

9 4.5 11.1245594 0.62046868 4.75 11.2796766

10 5 11.4149567 0.5426757 5.25 11.5506256

10

12


8/15

0 1 2

0

2

4

6

8


9/15

k3 k4

k2 x y k3 x y

-1.75 0.25 3.5625 -1.78125 0.5 3.109375

-1.36291504 0.75 2.77450562 -1.38725281 1 2.42160797

-1.06144994 1.25 2.16080882 -1.08040441 1.5 1.8859691

-0.82666634 1.75 1.68285648 -0.84142824 2 1.46880894

-0.64381485 2.25 1.31062309 -0.65531154 2.5 1.14392103

-0.50140854 2.75 1.02072452 -0.51036226 3 0.89089553

-0.39050128 3.25 0.79494903 -0.39747451 3.5 0.69383709-0.30412575 3.75 0.61911314 -0.30955657 4 0.54036629

-0.23685575 4.25 0.48217063 -0.24108532 4.5 0.42084191

-0.18446529 4.75 0.37551863 -0.18775932 5 0.3277553

-0.14366315 5.25 0.29245714 -0.14622857 5.5 0.25525864

k3 k4k2 x y k3 x y

1.715 0.25 6.42875 1.715125 0.5 6.8575625

1.54777774 0.75 7.24461475 1.54916501 1 7.63225282

1.38799697 1.25 7.97910492 1.39018764 1.5 8.3271995

1.2381273 1.75 8.6364178 1.24078901 2 8.94728048

1.09951879 2.25 9.2217448 1.10241425 2.5 9.49807223

0.97272949 2.75 9.74078373 0.97569243 3 9.98544757

0.85776931 3.25 10.1993963 0.86068619 3.5 10.4152971

0.75428045 3.75 10.6033737 0.75707658 4 10.7933419

0.66166961 4.25 10.9582809 0.66429866 4.5 11.1250128

0.57920396 4.75 11.2693604 0.58164001 5 11.4153794

0.50607968 5.25 11.5414766 0.5083113 5.5 11.6691123


10/15

3 4 5


11/15

yi +1k4

-1.5546875 3.11523438

-1.21080399 2.4261713

-0.94298455 1.88952306

-0.73440447 1.4715768

-0.57196051 1.14607666

-0.44544776 0.89257435

-0.34691855 0.69514457-0.27018314 0.54138457

-0.21042096 0.42163495

-0.16387765 0.32837293

-0.12762932 0.25573966

yi +1k4

1.63179375 6.85767031

1.46816336 7.63210567

1.31324324 8.32688598

1.16893496 8.9468651

1.03618623 9.49760136

0.91527618 9.98495402

0.80602716 10.4148036

0.70796081 10.7928635

0.62041196 11.1245594

0.54261064 11.4149567

0.47374043 11.6687232


12/15

6

y1

y2


13/15

x 0

y 1h 2

i x y k1

k2

x y

0 0 1 -1.1 1 -0.1

1 2 1.3440666667 3.8977933333 3 5.24186

2 4 3617.2096498 53896.423782 5 57513.633432

3 6 789315658.57 27547116484 7 28336432143

4 8 220E#015 1E#017 9 3E#017

5 10 27.45126E#024 117.52660E#024

6 121.03817E#0311.48354E#033 131.49393E#0337 145.50053E#0391.07205E#042 151.07755E#042

8 169.21603E#0482.34917E#051 172.35838E#051

9 184.22112E#0581.36300E#061 191.36722E#061

10 204.72139E#0681.88336E#071 211.88808E#071

0

0

50000000000000000000000000000000000000000000000000000000000000000000

100000000000000000000000000000000000000000000000000000000000000000000

150000000000000000000000000000000000000000000000000000000000000000000

200000000000000000000000000000000000000000000000000000000000000000000

250000000000000000000000000000000000000000000000000000000000000000000

300000000000000000000000000000000000000000000000000000000000000000000

350000000000000000000000000000000000000000000000000000000000000000000

400000000000000000000000000000000000000000000000000000000000000000000

450000000000000000000000000000000000000000000000000000000000000000000

500000000000000000000000000000000000000000000000000000000000000000000


14/15

k3 k4

k2 x y k3 x y

0.01 1 1.01 -0.101 2 0.798

41.410694 3 42.754760667 337.76260927 4 676.8692852

1374575.839 5 1378193.0487 32938813.863 6 65881244.936

5732E#012 7 5810E#012 0532E#013 8 0107E#014

#019 9 #019 21 10 21

9.02439E#026 119.02514E#0261.08211E#029 122.16423E#029

2.50830E#035 132.50841E#0354.21161E#037 148.42323E#0372.41264E#044 152.41270E#0445.40204E#046 161.08041E#047

6.78978E#053 176.78988E#0531.95481E#056 183.90961E#056

4.92063E#063 194.92067E#0631.77095E#066 203.54190E#066

8.30567E#073 218.30572E#0733.65369E#076 227.30737E#076

5 10 15 20


15/15

yi +1k4

2.3142 1.3440666667

10085.352349 3617.2096498

2299255448 789315658.57

374E#015 220E#015

2.23733E#023 2

3.09268E#0311.03817E#031

1.64169E#0405.50053E#0392.75396E#0499.21603E#048

1.26241E#0594.22112E#058

1.41286E#0694.72139E#068

3.52873E#0791.17868E#079

25

Col!" D

Runge Kutta de Cuarto Orden

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