georgepan

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9 years, 216 days

MaplePrimes Activity


These are questions asked by georgepan

Hello

I am trying to solve interactively the following DE with initial condiotion b(0)=1 and maple freezes as well as my pc.Can you help me?

Hello

I am trying to slve the second order differential equation with initial conditions  t0=0.dy/dt=0,y0=10000

-(diff(y, t, t))-9.81+0.563e-3*(0.1832e-2*abs(diff(y, t))+0.51702e-1*abs(diff(y, t))^(3/2)+.4*(diff(y, t))^2) = 0

using 4th order runge kutta.do i need to declare a step parameter like (D(y))(t) = u or is a command that can be applied automatically?

Thanks

 rk4.mw

I am trying to solve the folowing ODE with initial conditions t0=0,v0=0 and tf =80 with step 0.01 but the matrix that appears is not having the values!please help

f := proc (t, V) options operator, arrow; -9.81+0.563e-3*(0.1832e-2*abs(V)+0.51702e-1*(abs(V)^(3/2))+.4*V^2) end proc

V0 := 0:

t0 := 0:

tf := 80:

n := 1000

h := evalf((tf-t0)/n):

t := t0:

V := V0:

``

rk := proc (x0, tf, V0, n) local t, V, h, i, k1, k2, k3, k4, k, R; t := t0; V := V0; R := t, V; h := evalf((tf-t0)/n); for i to n do k1 := f(t, V); k2 := f(t+(1/2)*h, V+(1/2)*h*k1); k3 := f(t+(1/2)*h, V+(1/2)*h*k2); k4 := f(t+h, V+h*k3); k := (1/6)*k1+(1/3)*k2+(1/3)*k3+(1/6)*k4; V := V+h*k; t := t+h; R := R, t, V end do end proc:

R := rk(0, 80, 0, 300):

0, 0

 

.2666666667, -2.615998110

 

.5333333334, -5.231986045

 

.8000000001, -7.847954569

 

1.066666667, -10.46389463

 

1.333333334, -13.07979725

 

1.600000001, -15.69565351

 

1.866666668, -18.31145452

 

2.133333335, -20.92719143

 

2.400000002, -23.54285541

 

2.666666669, -26.15843764

 

2.933333336, -28.77392932

 

3.200000003, -31.38932166

 

3.466666670, -34.00460588

 

3.733333337, -36.61977321

 

4.000000004, -39.23481490

 

4.266666671, -41.84972219

 

4.533333338, -44.46448634

 

4.800000005, -47.07909861

 

5.066666672, -49.69355027

 

5.333333339, -52.30783259

 

5.600000006, -54.92193685

 

5.866666673, -57.53585433

 

6.133333340, -60.14957632

 

6.400000007, -62.76309410

 

6.666666674, -65.37639897

 

6.933333341, -67.98948223

 

7.200000008, -70.60233518

 

7.466666675, -73.21494912

 

7.733333342, -75.82731536

 

8.000000009, -78.43942520

 

8.266666676, -81.05126996

 

8.533333343, -83.66284095

 

8.800000010, -86.27412949

 

9.066666677, -88.88512689

 

9.333333344, -91.49582448

 

9.600000011, -94.10621358

 

9.866666678, -96.71628551

 

10.13333334, -99.32603160

 

10.40000001, -101.9354432

 

10.66666668, -104.5445116

 

10.93333335, -107.1532281

 

11.20000002, -109.7615841

 

11.46666669, -112.3695709

 

11.73333336, -114.9771799

 

12.00000003, -117.5844024

 

12.26666670, -120.1912297

 

12.53333337, -122.7976532

 

12.80000004, -125.4036642

 

13.06666671, -128.0092541

 

13.33333338, -130.6144142

 

13.60000005, -133.2191358

 

13.86666672, -135.8234103

 

14.13333339, -138.4272290

 

14.40000006, -141.0305833

 

14.66666673, -143.6334645

 

14.93333340, -146.2358640

 

15.20000007, -148.8377732

 

15.46666674, -151.4391834

 

15.73333341, -154.0400859

 

16.26666675, -159.2403334

 

16.53333342, -161.8396611

 

16.80000009, -164.4384465

 

17.06666676, -167.0366810

 

17.33333343, -169.6343560

 

17.60000010, -172.2314629

 

17.86666677, -174.8279930

 

18.13333344, -177.4239376

 

18.40000011, -180.0192882

 

18.66666678, -182.6140360

 

18.93333345, -185.2081725

 

19.20000012, -187.8016890

 

19.46666679, -190.3945769

 

19.73333346, -192.9868275

 

20.00000013, -195.5784322

 

20.26666680, -198.1693824

 

20.53333347, -200.7596694

 

20.80000014, -203.3492846

 

21.06666681, -205.9382194

 

21.33333348, -208.5264652

 

21.60000015, -211.1140133

 

21.86666682, -213.7008550

 

22.13333349, -216.2869818

 

22.40000016, -218.8723850

 

22.66666683, -221.4570560

 

22.93333350, -224.0409862

 

23.20000017, -226.6241669

 

23.46666684, -229.2065895

 

23.73333351, -231.7882454

 

24.00000018, -234.3691260

 

24.26666685, -236.9492226

 

24.53333352, -239.5285266

 

24.80000019, -242.1070294

 

25.06666686, -244.6847224

 

25.33333353, -247.2615969

 

25.60000020, -249.8376443

 

25.86666687, -252.4128560

 

26.13333354, -254.9872234

 

26.40000021, -257.5607378

 

26.66666688, -260.1333906

 

26.93333355, -262.7051732

 

27.20000022, -265.2760770

 

27.46666689, -267.8460934

 

27.73333356, -270.4152137

 

28.00000023, -272.9834293

 

28.26666690, -275.5507316

 

28.53333357, -278.1171120

 

28.80000024, -280.6825619

 

29.06666691, -283.2470726

 

29.33333358, -285.8106356

 

29.60000025, -288.3732422

 

29.86666692, -290.9348838

 

30.13333359, -293.4955517

 

30.40000026, -296.0552374

 

30.66666693, -298.6139322

 

30.93333360, -301.1716276

 

31.20000027, -303.7283149

 

31.46666694, -306.2839855

 

31.73333361, -308.8386307

 

32.00000028, -311.3922420

 

32.26666695, -313.9448108

 

32.53333362, -316.4963284

 

32.80000029, -319.0467862

 

33.06666696, -321.5961756

 

33.33333363, -324.1444880

 

33.60000030, -326.6917148

 

33.86666697, -329.2378474

 

34.13333364, -331.7828772

 

34.40000031, -334.3267955

 

34.66666698, -336.8695937

 

34.93333365, -339.4112633

 

35.20000032, -341.9517956

 

35.46666699, -344.4911820

 

35.73333366, -347.0294139

 

36.00000033, -349.5664827

 

36.26666700, -352.1023797

 

36.53333367, -354.6370964

 

36.80000034, -357.1706242

 

37.06666701, -359.7029544

 

37.33333368, -362.2340784

 

37.60000035, -364.7639877

 

37.86666702, -367.2926736

 

38.13333369, -369.8201275

 

38.40000036, -372.3463408

 

38.66666703, -374.8713049

 

38.93333370, -377.3950112

 

39.20000037, -379.9174511

 

39.46666704, -382.4386159

 

39.73333371, -384.9584971

 

40.00000038, -387.4770861

 

40.26666705, -389.9943742

 

40.53333372, -392.5103529

 

40.80000039, -395.0250135

 

41.06666706, -397.5383474

 

41.33333373, -400.0503461

 

41.60000040, -402.5610009

 

41.86666707, -405.0703032

 

42.13333374, -407.5782444

 

42.40000041, -410.0848159

 

42.66666708, -412.5900091

 

42.93333375, -415.0938154

 

43.20000042, -417.5962262

 

43.46666709, -420.0972329

 

43.73333376, -422.5968269

 

44.00000043, -425.0949996

 

44.26666710, -427.5917424

 

44.53333377, -430.0870466

 

44.80000044, -432.5809037

 

45.06666711, -435.0733051

 

45.33333378, -437.5642421

 

45.60000045, -440.0537062

 

45.86666712, -442.5416888

 

46.13333379, -445.0281812

 

46.40000046, -447.5131749

 

46.66666713, -449.9966612

 

46.93333380, -452.4786316

 

47.20000047, -454.9590775

 

47.46666714, -457.4379902

 

47.73333381, -459.9153612

 

48.00000048, -462.3911818

 

48.26666715, -464.8654435

 

48.53333382, -467.3381376

 

48.80000049, -469.8092556

 

49.06666716, -472.2787888

 

49.33333383, -474.7467287

 

49.60000050, -477.2130666

 

49.86666717, -479.6777940

 

50.13333384, -482.1409022

 

50.40000051, -484.6023827

 

50.66666718, -487.0622268

 

50.93333385, -489.5204260

 

51.20000052, -491.9769716

 

51.46666719, -494.4318551

 

51.73333386, -496.8850678

 

52.00000053, -499.3366012

 

52.26666720, -501.7864466

 

52.53333387, -504.2345955

 

52.80000054, -506.6810393

 

53.06666721, -509.1257693

 

53.33333388, -511.5687770

 

53.60000055, -514.0100537

 

53.86666722, -516.4495909

 

54.13333389, -518.8873800

 

54.40000056, -521.3234124

 

54.66666723, -523.7576794

 

54.93333390, -526.1901725

 

55.20000057, -528.6208831

 

55.46666724, -531.0498026

 

55.73333391, -533.4769224

 

56.00000058, -535.9022339

 

56.26666725, -538.3257285

 

56.53333392, -540.7473976

 

56.80000059, -543.1672326

 

57.06666726, -545.5852249

 

57.33333393, -548.0013659

 

57.60000060, -550.4156470

 

57.86666727, -552.8280597

 

58.13333394, -555.2385953

 

58.40000061, -557.6472452

 

58.66666728, -560.0540009

 

58.93333395, -562.4588537

 

59.20000062, -564.8617951

 

59.46666729, -567.2628164

 

59.73333396, -569.6619091

 

60.00000063, -572.0590645

 

60.26666730, -574.4542741

 

60.53333397, -576.8475293

 

60.80000064, -579.2388215

 

61.06666731, -581.6281420

 

61.33333398, -584.0154823

 

61.60000065, -586.4008338

 

61.86666732, -588.7841879

 

62.13333399, -591.1655361

 

62.40000066, -593.5448697

 

62.66666733, -595.9221801

 

62.93333400, -598.2974587

 

63.20000067, -600.6706970

 

63.46666734, -603.0418863

 

63.73333401, -605.4110181

 

64.00000068, -607.7780837

 

64.26666735, -610.1430746

 

64.53333402, -612.5059822

 

64.80000069, -614.8667979

 

65.06666736, -617.2255130

 

65.33333403, -619.5821190

 

65.60000070, -621.9366073

 

65.86666737, -624.2889694

 

66.13333404, -626.6391966

 

66.40000071, -628.9872803

 

66.66666738, -631.3332119

 

66.93333405, -633.6769829

 

67.20000072, -636.0185846

 

67.46666739, -638.3580085

 

67.73333406, -640.6952460

 

68.00000073, -643.0302885

 

68.26666740, -645.3631274

 

68.53333407, -647.6937540

 

68.80000074, -650.0221599

 

69.06666741, -652.3483364

 

69.33333408, -654.6722749

 

69.60000075, -656.9939668

 

69.86666742, -659.3134036

 

70.13333409, -661.6305766

 

70.40000076, -663.9454773

 

70.66666743, -666.2580971

 

70.93333410, -668.5684273

 

71.20000077, -670.8764594

 

71.46666744, -673.1821848

 

71.73333411, -675.4855950

 

72.00000078, -677.7866813

 

72.26666745, -680.0854351

 

72.53333412, -682.3818479

 

72.80000079, -684.6759110

 

73.06666746, -686.9676159

 

73.33333413, -689.2569539

 

73.60000080, -691.5439165

 

73.86666747, -693.8284951

 

74.13333414, -696.1106811

 

74.40000081, -698.3904660

 

74.66666748, -700.6678411

 

74.93333415, -702.9427978

 

75.20000082, -705.2153276

 

75.46666749, -707.4854218

 

75.73333416, -709.7530719

 

76.00000083, -712.0182693

 

76.26666750, -714.2810054

 

76.53333417, -716.5412716

 

76.80000084, -718.7990593

 

77.06666751, -721.0543600

 

77.33333418, -723.3071650

 

77.60000085, -725.5574658

 

77.86666752, -727.8052537

 

78.13333419, -730.0505202

 

78.40000086, -732.2932567

 

78.66666753, -734.5334546

 

78.93333420, -736.7711053

 

79.73333421, -743.4686884

 

``

 

 

Download runge_kutta4.mw

Hello

I want to plot in semilog graph the attached function.where b from 1 to 5 and R from 1 to 100000(in logR)I tried with the plot builder but i think i am doing smthing wrong

``

 

R = 2*b*(b^2-9*b-6)/(10*b^3+21*b^2+16*b+4)

(1)

;

 

 

 

;

;

 

 

Download re.mw

Hello

when i am trying to isolate for Rev in the following expression

the program doesnt respond.do you know why?

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