Lab 4 Group 5.sagews

#### Group 5 Lab 4 Grade: 20/20. Good job!!
def iterate(fcn,num_times,initial):
    count=srange(0,num_times)
    vals=[initial]
    for i in count:
        b=fcn(vals[i])
        vals.append(b)
    return vals

var("N")
h=0.1
g(N)=N+h*0.2*N*(1-N/100)
count=int(round(100/h))
L= iterate(g,count,10)

N

#Value of N at 100 is L[1000]
list_plot(L,plotjoined=True)
L[1000]
##### Good. -HK

99.9999984129133

N

var("N")
h=0.1
g(N)=N+h*0.2*N*(1-N/100)
count=int(round(100/h))
Ex2= iterate(g,count,20)

N

var("N")
h=0.1
g(N)=N+h*0.2*N*(1-N/100)
count=int(round(100/h))
Ex2a= iterate(g,count,150)

N

Ex2a

#Exercise 3

def iterate(fcn,num_times,initial):
    count=srange(0,num_times)
    vals=[initial]
    for i in count:
        b=fcn(vals[i])
        vals.append(b)
    return vals

var("N")
h=0.1
g(N)=N+h*0.2*N*(1-N/100)
count=int(round(100/h))
L= iterate(g,count,10)
L[100]

tfinal=srange(0,100+h,h)
list_plot(zip(tfinal, L)) ##### Good. -HK

[150, 148.500000000000, 147.059550000000, 145.675438750759, 144.344680834729, 143.064497074368, 141.832296951227, 140.645662798559, 139.502335561721, 138.400201947521, 137.337282806648, 136.311722613039, 135.321779920953, 134.365818695177, 133.442300422355, 132.549776922400, 131.686883788413, 130.852334391800, 130.044914396480, 129.263476732332, 128.506936983592, 127.774269152683, 127.064501764236, 126.376714277802, 125.710033781028, 125.063631938003, 124.436722170058, 123.828557048574, 123.238425881399, 122.665652476282, 122.109593066321, 121.569634383883, 121.045191870714, 120.535708013125, 120.040650792142, 119.559512239465, 119.091807090867, 118.637071529450, 118.194862011823, 117.764754170860, 117.346341789293, 116.939235838813, 116.543063579876, 116.157467717757, 115.782105610792, 115.416648527074, 115.060780946171, 114.714199902706, 114.376614368896, 114.047744673376, 113.727321953827, 113.415087641145, 113.110792973039, 112.814198535101, 112.525073827580, 112.243196856151, 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#It comes up with an error if zip is not used

#Exercise 4
def iterate(fcn,num_times,initial):
    count=srange(0,num_times)
    vals=[initial]
    for i in count:
        b=fcn(vals[i])
        vals.append(b)
    return vals

def euler1(diff_eq, initial, h, num_times):
    fcn(N)=N+h*diff_eq(N)
    ex4out=iterate(fcn, num_times, initial)
    return ex4out

N_prime(N)=0.2*N*(1-N/100)
h=0.1
out4=euler1(N_prime, 10, h, 1000)

out4

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#Exercise 5
def euler2(diff_eq, initial, h, num_times):
    fcn(N)=N+h*diff_eq(N)
    ex5out=iterate(fcn, num_times, initial)
    tfinal=srange(0,100+h,h)
    Ex5=zip(tfinal, ex5out)
    return Ex5

N_prime(N)=0.2*N*(1-N/100)
h=0.1
out5=euler2(N_prime, 10, h, 1000) ##### Good. -HK

out5

[(0.000000000000000, 10), (0.100000000000000, 10.1800000000000), (0.200000000000000, 10.3628735200000), (0.300000000000000, 10.5486531608817), (0.400000000000000, 10.7373714073976), (0.500000000000000, 10.9290606065975), (0.600000000000000, 11.1237529455809), (0.700000000000000, 11.3214804285737), (0.800000000000000, 11.5222748533262), (0.900000000000000, 11.7261677868336), (1.00000000000000, 11.9331905403773), (1.10000000000000, 12.1433741438903), (1.20000000000000, 12.3567493196484), (1.30000000000000, 12.5733464552916), (1.40000000000000, 12.7931955761805), (1.50000000000000, 13.0163263170940), (1.60000000000000, 13.2427678932773), (1.70000000000000, 13.4725490708478), (1.80000000000000, 13.7056981365714), (1.90000000000000, 13.9422428670207), (2.00000000000000, 14.1822104971285), (2.10000000000000, 14.4256276881541), (2.20000000000000, 14.6725204950778), (2.30000000000000, 14.9229143334436), (2.40000000000000, 15.1768339456718), (2.50000000000000, 15.4343033668624), (2.60000000000000, 15.6953458901155), (2.70000000000000, 15.9599840313958), (2.80000000000000, 16.2282394939672), (2.90000000000000, 16.5001331324319), (3.00000000000000, 16.7756849164029), (3.10000000000000, 17.0549138938481), (3.20000000000000, 17.3378381541397), (3.30000000000000, 17.6244747908507), (3.40000000000000, 17.9148398643370), (3.50000000000000, 18.2089483641508), (3.60000000000000, 18.5068141713282), (3.70000000000000, 18.8084500206003), (3.80000000000000, 19.1138674625768), (3.90000000000000, 19.4230768259530), (4.00000000000000, 19.7360871797947), (4.10000000000000, 20.0529062959569), (4.20000000000000, 20.3735406116931), (4.30000000000000, 20.6979951925157), (4.40000000000000, 21.0262736953681), (4.50000000000000, 21.3583783321730), (4.60000000000000, 21.6943098338204), (4.70000000000000, 22.0340674146637), (4.80000000000000, 22.3776487375901), (4.90000000000000, 22.7250498797374), (5.00000000000000, 23.0762652989248), (5.10000000000000, 23.4312878008740), 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(85.7999999999994, 99.9999720425348), (85.8999999999994, 99.9999726016840), (85.9999999999994, 99.9999731496501), (86.0999999999994, 99.9999736866570), (86.1999999999994, 99.9999742129237), (86.2999999999994, 99.9999747286651), (86.3999999999994, 99.9999752340917), (86.4999999999994, 99.9999757294097), (86.5999999999994, 99.9999762148214), (86.6999999999993, 99.9999766905249), (86.7999999999993, 99.9999771567143), (86.8999999999993, 99.9999776135799), (86.9999999999993, 99.9999780613082), (87.0999999999993, 99.9999785000819), (87.1999999999993, 99.9999789300802), (87.2999999999993, 99.9999793514785), (87.3999999999993, 99.9999797644488), (87.4999999999993, 99.9999801691598), (87.5999999999993, 99.9999805657765), (87.6999999999993, 99.9999809544609), (87.7999999999993, 99.9999813353716), (87.8999999999993, 99.9999817086641), (87.9999999999993, 99.9999820744907), (88.0999999999993, 99.9999824330009), (88.1999999999993, 99.9999827843408), (88.2999999999993, 99.9999831286539), (88.3999999999993, 99.9999834660808), (88.4999999999992, 99.9999837967591), (88.5999999999992, 99.9999841208239), (88.6999999999992, 99.9999844384074), (88.7999999999992, 99.9999847496392), (88.8999999999992, 99.9999850546463), (88.9999999999992, 99.9999853535534), (89.0999999999992, 99.9999856464822), (89.1999999999992, 99.9999859335526), (89.2999999999992, 99.9999862148815), (89.3999999999992, 99.9999864905838), (89.4999999999992, 99.9999867607721), (89.5999999999992, 99.9999870255566), (89.6999999999992, 99.9999872850454), (89.7999999999992, 99.9999875393445), (89.8999999999992, 99.9999877885575), (89.9999999999992, 99.9999880327864), (90.0999999999992, 99.9999882721306), (90.1999999999992, 99.9999885066880), (90.2999999999991, 99.9999887365542), (90.3999999999991, 99.9999889618231), (90.4999999999991, 99.9999891825866), (90.5999999999991, 99.9999893989348), (90.6999999999991, 99.9999896109561), (90.7999999999991, 99.9999898187370), (90.8999999999991, 99.9999900223622), (90.9999999999991, 99.9999902219149), (91.0999999999991, 99.9999904174766), (91.1999999999991, 99.9999906091271), (91.2999999999991, 99.9999907969445), (91.3999999999991, 99.9999909810056), (91.4999999999991, 99.9999911613855), (91.5999999999991, 99.9999913381577), (91.6999999999991, 99.9999915113946), (91.7999999999991, 99.9999916811666), (91.8999999999991, 99.9999918475433), (91.9999999999990, 99.9999920105924), (92.0999999999990, 99.9999921703806), (92.1999999999990, 99.9999923269729), (92.2999999999990, 99.9999924804335), (92.3999999999990, 99.9999926308248), (92.4999999999990, 99.9999927782083), (92.5999999999990, 99.9999929226441), (92.6999999999990, 99.9999930641912), (92.7999999999990, 99.9999932029074), (92.8999999999990, 99.9999933388492), (92.9999999999990, 99.9999934720722), (93.0999999999990, 99.9999936026308), (93.1999999999990, 99.9999937305782), (93.2999999999990, 99.9999938559666), (93.3999999999990, 99.9999939788472), (93.4999999999990, 99.9999940992703), (93.5999999999990, 99.9999942172849), (93.6999999999990, 99.9999943329392), (93.7999999999989, 99.9999944462804), (93.8999999999989, 99.9999945573548), (93.9999999999989, 99.9999946662077), (94.0999999999989, 99.9999947728835), (94.1999999999989, 99.9999948774258), (94.2999999999989, 99.9999949798773), (94.3999999999989, 99.9999950802798), (94.4999999999989, 99.9999951786742), (94.5999999999989, 99.9999952751007), (94.6999999999989, 99.9999953695987), (94.7999999999989, 99.9999954622067), (94.8999999999989, 99.9999955529625), (94.9999999999989, 99.9999956419033), (95.0999999999989, 99.9999957290652), (95.1999999999989, 99.9999958144839), (95.2999999999989, 99.9999958981942), (95.3999999999989, 99.9999959802304), (95.4999999999988, 99.9999960606257), (95.5999999999988, 99.9999961394132), (95.6999999999988, 99.9999962166250), (95.7999999999988, 99.9999962922925), (95.8999999999988, 99.9999963664466), (95.9999999999988, 99.9999964391177), (96.0999999999988, 99.9999965103353), (96.1999999999988, 99.9999965801286), (96.2999999999988, 99.9999966485260), (96.3999999999988, 99.9999967155555), (96.4999999999988, 99.9999967812444), (96.5999999999988, 99.9999968456195), (96.6999999999988, 99.9999969087071), (96.7999999999988, 99.9999969705330), (96.8999999999988, 99.9999970311223), (96.9999999999988, 99.9999970904999), (97.0999999999988, 99.9999971486899), (97.1999999999988, 99.9999972057161), (97.2999999999987, 99.9999972616018), (97.3999999999987, 99.9999973163697), (97.4999999999987, 99.9999973700423), (97.5999999999987, 99.9999974226415), (97.6999999999987, 99.9999974741887), (97.7999999999987, 99.9999975247049), (97.8999999999987, 99.9999975742108), (97.9999999999987, 99.9999976227266), (98.0999999999987, 99.9999976702720), (98.1999999999987, 99.9999977168666), (98.2999999999987, 99.9999977625293), (98.3999999999987, 99.9999978072787), (98.4999999999987, 99.9999978511331), (98.5999999999987, 99.9999978941105), (98.6999999999987, 99.9999979362282), (98.7999999999987, 99.9999979775037), (98.8999999999987, 99.9999980179536), (98.9999999999986, 99.9999980575945), (99.0999999999986, 99.9999980964426), (99.1999999999986, 99.9999981345138), (99.2999999999986, 99.9999981718235), (99.3999999999986, 99.9999982083870), (99.4999999999986, 99.9999982442193), (99.5999999999986, 99.9999982793349), (99.6999999999986, 99.9999983137482), (99.7999999999986, 99.9999983474732), (99.8999999999986, 99.9999983805238), (99.9999999999986, 99.9999984129133)]

#Exercise 6
def euler3(diff_eq, initial, h, tfinal):
    steps=int(round(tfinal/h))
    fcn(N)=N+h*diff_eq(N)
    ex6out=iterate(fcn, steps, initial)
    times=srange(0, tfinal, h)
    Ex6=zip(times, ex6out)
    return Ex6

N_prime(N)=0.2*N*(1-N/100)
h=0.1
out6=euler3(N_prime, 10, h, 100)

out6

[(0.000000000000000, 10), (0.100000000000000, 10.1800000000000), (0.200000000000000, 10.3628735200000), (0.300000000000000, 10.5486531608817), (0.400000000000000, 10.7373714073976), (0.500000000000000, 10.9290606065975), (0.600000000000000, 11.1237529455809), (0.700000000000000, 11.3214804285737), (0.800000000000000, 11.5222748533262), (0.900000000000000, 11.7261677868336), (1.00000000000000, 11.9331905403773), (1.10000000000000, 12.1433741438903), (1.20000000000000, 12.3567493196484), (1.30000000000000, 12.5733464552916), (1.40000000000000, 12.7931955761805), (1.50000000000000, 13.0163263170940), (1.60000000000000, 13.2427678932773), (1.70000000000000, 13.4725490708478), (1.80000000000000, 13.7056981365714), (1.90000000000000, 13.9422428670207), (2.00000000000000, 14.1822104971285), (2.10000000000000, 14.4256276881541), (2.20000000000000, 14.6725204950778), (2.30000000000000, 14.9229143334436), (2.40000000000000, 15.1768339456718), (2.50000000000000, 15.4343033668624), (2.60000000000000, 15.6953458901155), (2.70000000000000, 15.9599840313958), (2.80000000000000, 16.2282394939672), (2.90000000000000, 16.5001331324319), (3.00000000000000, 16.7756849164029), (3.10000000000000, 17.0549138938481), (3.20000000000000, 17.3378381541397), (3.30000000000000, 17.6244747908507), (3.40000000000000, 17.9148398643370), (3.50000000000000, 18.2089483641508), (3.60000000000000, 18.5068141713282), (3.70000000000000, 18.8084500206003), (3.80000000000000, 19.1138674625768), (3.90000000000000, 19.4230768259530), (4.00000000000000, 19.7360871797947), (4.10000000000000, 20.0529062959569), (4.20000000000000, 20.3735406116931), (4.30000000000000, 20.6979951925157), (4.40000000000000, 21.0262736953681), (4.50000000000000, 21.3583783321730), (4.60000000000000, 21.6943098338204), (4.70000000000000, 22.0340674146637), (4.80000000000000, 22.3776487375901), (4.90000000000000, 22.7250498797374), (5.00000000000000, 23.0762652989248), (5.10000000000000, 23.4312878008740), (5.20000000000000, 23.7901085072900), (5.30000000000000, 24.1527168248781), (5.40000000000000, 24.5191004153711), (5.50000000000000, 24.8892451666427), (5.60000000000000, 25.2631351649825), (5.70000000000000, 25.6407526686093), (5.80000000000000, 26.0220780824990), (5.90000000000000, 26.4070899346026), (5.99999999999999, 26.7957648535318), (6.09999999999999, 27.1880775477853), (6.19999999999999, 27.5840007865921), (6.29999999999999, 27.9835053824450), (6.39999999999999, 28.3865601753961), (6.49999999999999, 28.7931320191857), (6.59999999999999, 29.2031857692746), (6.69999999999999, 29.6166842728451), (6.79999999999999, 30.0335883608386), (6.89999999999999, 30.4538568420897), (6.99999999999999, 30.8774464996198), (7.09999999999999, 31.3043120891448), (7.19999999999999, 31.7344063398528), (7.29999999999999, 32.1676799575012), (7.39999999999999, 32.6040816298816), (7.49999999999999, 33.0435580346936), (7.59999999999999, 33.4860538498691), (7.69999999999999, 33.9315117663792), (7.79999999999999, 34.3798725035564), (7.89999999999999, 34.8310748269554), (7.99999999999999, 35.2850555687743), (8.09999999999999, 35.7417496508515), (8.19999999999999, 36.2010901102477), (8.29999999999999, 36.6630081274186), (8.39999999999999, 37.1274330569767), (8.49999999999999, 37.5942924610362), (8.59999999999999, 38.0635121451277), (8.69999999999999, 38.5350161966658), (8.79999999999998, 39.0087270259437), (8.89999999999998, 39.4845654096256), (8.99999999999998, 39.9624505367008), (9.09999999999998, 40.4423000568551), (9.19999999999998, 40.9240301312145), (9.29999999999998, 41.4075554854027), (9.39999999999998, 41.8927894648554), (9.49999999999998, 42.3796440923231), (9.59999999999998, 42.8680301274912), (9.69999999999998, 43.3578571286387), (9.79999999999998, 43.8490335162540), (9.89999999999998, 44.3414666385172), (9.99999999999998, 44.8350628385566), (10.1000000000000, 45.3297275233803), (10.2000000000000, 45.8253652343791), (10.3000000000000, 46.3218797192938), (10.4000000000000, 46.8191740055340), (10.5000000000000, 47.3171504747325), (10.6000000000000, 47.8157109384175), (10.7000000000000, 48.3147567146766), (10.8000000000000, 48.8141887056904), (10.9000000000000, 49.3139074760053), (11.0000000000000, 49.8138133314150), (11.1000000000000, 50.3138063983199), (11.2000000000000, 50.8137867034288), (11.3000000000000, 51.3136542536690), (11.4000000000000, 51.8133091161694), (11.5000000000000, 52.3126514981792), (11.6000000000000, 52.8115818267888), (11.7000000000000, 53.3100008283151), (11.8000000000000, 53.8078096072184), (11.9000000000000, 54.3049097244174), (12.0000000000000, 54.8012032748703), (12.1000000000000, 55.2965929642930), (12.2000000000000, 55.7909821848871), (12.3000000000000, 56.2842750899540), (12.4000000000000, 56.7763766672728), (12.5000000000000, 57.2671928111254), (12.6000000000000, 57.7566303928546), (12.7000000000000, 58.2445973298443), (12.8000000000000, 58.7310026528181), (12.9000000000000, 59.2157565713534), (13.0000000000000, 59.6987705375169), (13.1000000000000, 60.1799573075290), (13.2000000000000, 60.6592310013724), (13.3000000000000, 61.1365071602642), (13.4000000000000, 61.6117028019181), (13.5000000000000, 62.0847364735261), (13.6000000000000, 62.5555283023992), (13.7000000000000, 63.0240000442087), (13.8000000000000, 63.4900751287784), (13.9000000000000, 63.9536787033824), (14.0000000000000, 64.4147376735109), (14.1000000000000, 64.8731807410717), (14.2000000000000, 65.3289384400004), (14.3000000000000, 65.7819431692609), (14.4000000000000, 66.2321292232214), (14.5000000000000, 66.6794328193975), (14.6000000000000, 67.1237921235621), (14.7000000000000, 67.5651472722240), (14.8000000000000, 68.0034403924850), (14.9000000000000, 68.4386156192918), (15.0000000000000, 68.8706191101006), (15.1000000000000, 69.2993990569809), (15.2000000000000, 69.7249056961888), (15.3000000000000, 70.1470913152441), (15.4000000000000, 70.5659102575511), (15.5000000000000, 70.9813189246068), (15.6000000000000, 71.3932757758436), (15.7000000000000, 71.8017413261593), (15.8000000000000, 72.2066781411888), (15.9000000000000, 72.6080508303755), (16.0000000000000, 73.0058260379057), (16.1000000000000, 73.3999724315685), (16.2000000000000, 73.7904606896088), (16.3000000000000, 74.1772634856441), (16.4000000000000, 74.5603554717132), (16.5000000000000, 74.9397132595338), (16.6000000000000, 75.3153154000403), (16.7000000000000, 75.6871423612796), (16.8000000000000, 76.0551765047418), (16.9000000000000, 76.4194020602032), (17.0000000000000, 76.7798050991594), (17.1000000000000, 77.1363735069297), (17.2000000000000, 77.4890969535081), (17.3000000000000, 77.8379668632443), (17.4000000000000, 78.1829763834284), (17.5000000000000, 78.5241203518627), (17.6000000000000, 78.8613952634932), (17.7000000000000, 79.1947992361820), (17.8000000000000, 79.5243319756938), (17.9000000000000, 79.8499947399716), (18.0000000000000, 80.1717903027764), (18.1000000000000, 80.4897229167615), (18.2000000000000, 80.8037982760533), (18.3000000000000, 81.1140234784069), (18.4000000000000, 81.4204069870039), (18.5000000000000, 81.7229585919581), (18.6000000000000, 82.0216893715927), (18.7000000000000, 82.3166116535506), (18.8000000000000, 82.6077389757973), (18.9000000000000, 82.8950860475745), (19.0000000000000, 83.1786687103591), (19.1000000000000, 83.4585038988807), (19.2000000000000, 83.7346096022504), (19.3000000000000, 84.0070048252472), (19.4000000000000, 84.2757095498103), (19.5000000000000, 84.5407446967817), (19.6000000000000, 84.8021320879401), (19.7000000000000, 85.0598944083668), (19.8000000000000, 85.3140551691816), (19.9000000000000, 85.5646386706832), (20.0000000000000, 85.8116699659280), (20.1000000000000, 86.0551748247783), (20.2000000000000, 86.2951796984492), (20.3000000000000, 86.5317116845807), (20.4000000000000, 86.7647984928596), (20.5000000000000, 86.9944684112155), (20.6000000000000, 87.2207502726098), (20.7000000000000, 87.4436734224386), (20.8000000000000, 87.6632676865654), (20.9000000000000, 87.8795633399994), (21.0000000000000, 88.0925910762336), (21.1000000000000, 88.3023819772534), (21.2000000000000, 88.5089674842271), (21.3000000000000, 88.7123793688868), (21.4000000000000, 88.9126497056067), (21.5000000000000, 89.1098108441845), (21.6000000000000, 89.3038953833309), (21.7000000000000, 89.4949361448701), (21.8000000000000, 89.6829661486526), (21.9000000000000, 89.8680185881816), (22.0000000000000, 90.0501268069521), (22.1000000000000, 90.2293242755015), (22.2000000000000, 90.4056445691688), (22.3000000000000, 90.5791213465588), (22.4000000000000, 90.7497883287071), (22.5000000000000, 90.9176792789402), (22.6000000000001, 91.0828279834253), (22.7000000000001, 91.2452682324022), (22.8000000000001, 91.4050338020896), (22.9000000000001, 91.5621584372592), (23.0000000000001, 91.7166758344664), (23.1000000000001, 91.8686196259308), (23.2000000000001, 92.0180233640546), (23.3000000000001, 92.1649205065702), (23.4000000000001, 92.3093444023051), (23.5000000000001, 92.4513282775545), (23.6000000000001, 92.5909052230488), (23.7000000000001, 92.7281081815050), (23.8000000000001, 92.8629699357510), (23.9000000000001, 92.9955230974084), (24.0000000000001, 93.1258000961244), (24.1000000000001, 93.2538331693382), (24.2000000000001, 93.3796543525700), (24.3000000000001, 93.5032954702203), (24.4000000000001, 93.6247881268665), (24.5000000000001, 93.7441636990437), (24.6000000000001, 93.8614533274979), (24.7000000000001, 93.9766879098979), (24.8000000000001, 94.0898980939930), (24.9000000000001, 94.2011142712052), (25.0000000000001, 94.3103665706420), (25.1000000000001, 94.4176848535171), (25.2000000000001, 94.5230987079678), (25.3000000000001, 94.6266374442559), (25.4000000000001, 94.7283300903397), (25.5000000000001, 94.8282053878057), (25.6000000000001, 94.9262917881474), (25.7000000000001, 95.0226174493806), (25.8000000000001, 95.1172102329820), (25.9000000000001, 95.2100977011406), 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(98.7999999999987, 99.9999979775037), (98.8999999999987, 99.9999980179536), (98.9999999999986, 99.9999980575945), (99.0999999999986, 99.9999980964426), (99.1999999999986, 99.9999981345138), (99.2999999999986, 99.9999981718235), (99.3999999999986, 99.9999982083870), (99.4999999999986, 99.9999982442193), (99.5999999999986, 99.9999982793349), (99.6999999999986, 99.9999983137482), (99.7999999999986, 99.9999983474732), (99.8999999999986, 99.9999983805238)]

#Exercise 7

diff_eq1(N)=0.05*N
def euler4(diff_eq, initial, h, tfinal):
    steps=int(round(tfinal/h))
    times=srange(0,steps+h,h)
    count=srange(0,steps) #his line added by Hannah
    vals=[initial]
    tlist=srange(0,tfinal,h)
    for i in count:
        vals.append(vals[i]+h*diff_eq(vals[i]))
    return zip(tfinal, vals)

part1=euler4(diff_eq1, 10, 0.1, 100)
part2=euler4(diff_eq1, 10, 1, 100)
part3=euler4(diff_eq1, 10, 0.01, 100)