Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I am trying to use Maple to view some 120,000 x 120,000 matrices with rational entries on a linux box with 504GB of RAM. Unfortunately when I run the command

read "/home/user/source_file.txt"

maple issues an Execution stopped: Stack limit reached error. Running the kernelopts command seems to indicate that the default stack limit is 8160 on this system. I have tried setting

kernelopts(stacklimit=13560)

but the same error is always issued at around 7 GB of RAM usage (according to htop). Is there any way around this in Maple?

How to solve the given system of equations using the collocation method. I already tried numerical method. 

Kindly help me.

restart:

with(plots):

M := 0.1e-1;

0.1e-1

 

6.3

 

1

(1)

de1 := diff(y(x), `$`(x, 3))+y(x)*(diff(y(x), `$`(x, 2)))-(diff(y(x), `$`(x, 2)))^2-M*(diff(y(x), x)) = 0;

diff(diff(diff(y(x), x), x), x)+y(x)*(diff(diff(y(x), x), x))-(diff(diff(y(x), x), x))^2-0.1e-1*(diff(y(x), x)) = 0

(2)

de2 := (diff(z(x), `$`(x, 2)))/Pr+y(x)*(diff(z(x), x))+Hs*z(x) = 0

.1587301587*(diff(diff(z(x), x), x))+y(x)*(diff(z(x), x))+z(x) = 0

(3)

bc := y(0) = 0, (D(y))(0) = 1, (D(y))(5) = 0, z(0) = 1, z(5) = 0;

y(0) = 0, (D(y))(0) = 1, (D(y))(5) = 0, z(0) = 1, z(5) = 0

(4)

sol := dsolve(eval([de1, de2, bc]), numeric);

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(50, {(1) = .0, (2) = 0.538450712436539e-1, (3) = .1082766859915131, (4) = .16331444031270473, (5) = .2189790463606035, (6) = .2752924234461127, (7) = .33227779889470094, (8) = .38995982000331736, (9) = .4483646786278111, (10) = .5075202501873479, (11) = .5674562491788733, (12) = .6282044036635384, (13) = .6897986516330131, (14) = .7524176453724036, (15) = .816715733668989, (16) = .8829036702135253, (17) = .9511585880378444, (18) = 1.0216871515791115, (19) = 1.0947329467114486, (20) = 1.170586433436612, (21) = 1.2495986390793312, (22) = 1.3322004686809672, (23) = 1.4189307352844525, (24) = 1.5100425310518173, (25) = 1.605556044446249, (26) = 1.706170701849191, (27) = 1.8128032039007311, (28) = 1.9266829029680352, (29) = 2.049525210932362, (30) = 2.1836360719075385, (31) = 2.3285917464945434, (32) = 2.485839068288575, (33) = 2.6591632259916818, (34) = 2.8548144648261875, (35) = 3.0721020019341, (36) = 3.305701178649673, (37) = 3.559949463816246, (38) = 3.7970789219278824, (39) = 3.990153302379728, (40) = 4.15720355507037, (41) = 4.306208343595448, (42) = 4.427174986030093, (43) = 4.526423733667591, (44) = 4.612636841962476, (45) = 4.689904237648306, (46) = 4.7605405732587975, (47) = 4.826006890793816, (48) = 4.88729546673539, (49) = 4.945116721690995, (50) = 5.0}, datatype = float[8], order = C_order); Y := Matrix(50, 5, {(1, 1) = .0, (1, 2) = 1.0, (1, 3) = -1.016912631477338, (1, 4) = 1.0, (1, 5) = 4.938383111325546, (2, 1) = 0.5239768838140454e-1, (2, 2) = .9467292622483128, (2, 3) = -.9622772113928727, (2, 4) = 1.2552137152775404, (2, 5) = 4.513346170739063, (3, 1) = .10253029316475297, (3, 2) = .895783706943777, (3, 3) = -.9101344320647631, (3, 4) = 1.4856388355002517, (3, 5) = 3.9305405877166715, (4, 1) = .1504792351703645, (4, 2) = .8470745536097423, (4, 3) = -.860373451742725, (4, 4) = 1.6829551945815935, (4, 5) = 3.223524805389885, (5, 1) = .19632323217740202, (5, 2) = .8005166268083528, (5, 3) = -.8128903023040563, (5, 4) = 1.8406334092867063, (5, 5) = 2.4329926016781056, (6, 1) = .24013840636663933, (6, 2) = .75602811722521, (6, 3) = -.7675871163117387, (6, 4) = 1.9543101701250922, (6, 5) = 1.6030729437227047, (7, 1) = .2819983835793791, (7, 2) = .7135303716905912, (7, 3) = -.7243714778269336, (7, 4) = 2.021973234344372, (7, 5) = .7775670166921098, (8, 1) = .3219743854445238, (8, 2) = .6729477074610013, (8, 3) = -.6831558741457402, (8, 4) = 2.04395171767529, (8, 5) = -0.34653255090257517e-2, (9, 1) = .36013531525388137, (9, 2) = .6342072469341395, (9, 3) = -.6438572302054374, (9, 4) = 2.0227281462789084, (9, 5) = -.7064433677651218, (10, 1) = .3965478383244555, (10, 2) = .5972387696518396, (10, 3) = -.6063965109971585, (10, 4) = 1.9626055145558932, (10, 5) = -1.3061198107940517, (11, 1) = .4312764574697176, (11, 2) = .5619745789945647, (11, 3) = -.5706983801552904, (11, 4) = 1.8692736251817776, (11, 5) = -1.786473233829117, (12, 1) = .46438358410487035, (12, 2) = .528349381415236, (12, 3) = -.5366909051394194, (12, 4) = 1.7493236289925442, (12, 5) = -2.1406810006817762, (13, 1) = .49592960543014786, (13, 2) = .49630017642071433, (13, 3) = -.5043053012120328, (13, 4) = 1.6097582709295248, (13, 5) = -2.3703112091517946, (14, 1) = .5260392137265275, (14, 2) = .46569879325333513, (14, 3) = -.4734077198356524, (14, 4) = 1.4571855527545918, (14, 5) = -2.4840706437151705, (15, 1) = .5550249899686894, (15, 2) = .4362259970506212, (15, 3) = -.44367242988215233, (15, 4) = 1.2966009526912445, (15, 5) = -2.4948251356156317, (16, 1) = .582947323077621, (16, 2) = .4078186772916242, (16, 3) = -.41503308219069956, (16, 4) = 1.133618168947713, (16, 5) = -2.4170112399060972, (17, 1) = .6098379764681325, (17, 2) = .3804427617884565, (17, 3) = -.3874529846540737, (17, 4) = .9734125833836331, (17, 5) = -2.267713799142949, (18, 1) = .6357288212995027, (18, 2) = .35406397565685854, (18, 3) = -.3608955340280772, (18, 4) = .8203928722713415, (18, 5) = -2.0653717123140347, (19, 1) = .6606520558243368, (19, 2) = .32864756458000216, (19, 3) = -.33532390992055233, (19, 4) = .6780764948146691, (19, 5) = -1.8284211343980543, (20, 1) = .6846405020881483, (20, 2) = .30415792526822016, (20, 3) = -.310700681058048, (20, 4) = .5490330762061609, (20, 5) = -1.5741295655423746, (21, 1) = .7077280179775027, (21, 2) = .2805580974006707, (21, 3) = -.2869872780487047, (21, 4) = .4348909698491685, (21, 5) = -1.3176869854655087, (22, 1) = .7299500860736533, (22, 2) = .25780904339388555, (22, 3) = -.2641432592769831, (22, 4) = .33639815254557953, (22, 5) = -1.071588245625372, (23, 1) = .7513446824807472, (23, 2) = .2358685927532746, (23, 3) = -.2421252475321414, (23, 4) = .2535257527268136, (23, 5) = -.845310470542935, (24, 1) = .7718600373416271, (24, 2) = .2147861043754655, (24, 3) = -.2209818389817886, (24, 4) = .18588236390672697, (24, 5) = -.6461214157898081, (25, 1) = .7913984364444584, (25, 2) = .1946582172929835, (25, 3) = -.20080896597698863, (25, 4) = .13250101521230842, (25, 5) = -.47835610933187955, (26, 1) = .8100007854235601, (26, 2) = .1754386620756086, (26, 3) = -.18155930417548316, (26, 4) = 0.9154569608003324e-1, (26, 5) = -.3421381651798363, (27, 1) = .8277118076501322, (27, 2) = .15707596816855374, (27, 3) = -.16318052643948905, (27, 4) = 0.6105466126293412e-1, (27, 5) = -.23553722921336775, (28, 1) = .8445805217874315, (28, 2) = .13951234873701424, (28, 3) = -.14561421333147123, (28, 4) = 0.39087681110023476e-1, (28, 5) = -.15525672367643156, (29, 1) = .8606634863301678, (29, 2) = .12267930610986412, (29, 3) = -.12879150739256892, (29, 4) = 0.23832991063636576e-1, (29, 5) = -0.9724838130607329e-1, (30, 1) = .8760079352865905, (30, 2) = .10651370141941992, (30, 3) = -.1126492397968819, (30, 4) = 0.13691444825679132e-1, (30, 5) = -0.5727653723318041e-1, (31, 1) = .8903192581096104, (31, 2) = 0.9131052167272624e-1, (31, 3) = -0.9748175032923309e-1, (31, 4) = 0.74131272943985405e-2, (31, 5) = -0.3172088613075896e-1, (32, 1) = .9035329750439559, (32, 2) = 0.7712276927556598e-1, (32, 3) = -0.8334133909913169e-1, (32, 4) = 0.3755698608845979e-2, (32, 5) = -0.1640104680740198e-1, (33, 1) = .9157173948547132, (33, 2) = 0.6385549523046109e-1, (33, 3) = -0.7013295494960084e-1, (33, 4) = 0.17491668487648983e-2, (33, 5) = -0.7780056793655609e-2, (34, 1) = .9269514730577374, (34, 2) = 0.51386320628059305e-1, (34, 3) = -0.57734884774429875e-1, (34, 4) = 0.7271289957321933e-3, (34, 5) = -0.32884474837452868e-2, (35, 1) = .9368471128429581, (35, 2) = 0.4010243173621042e-1, (35, 3) = -0.4653193161278045e-1, (35, 4) = 0.27013268380656147e-3, (35, 5) = -0.12396732969434932e-2, (36, 1) = .9450380185477333, (36, 2) = 0.30399509190318585e-1, (36, 3) = -0.36915005251636664e-1, (36, 4) = 0.9182614553853198e-4, (36, 5) = -0.42674003103921183e-3, (37, 1) = .9516679912394145, (37, 2) = 0.22101471191290013e-1, (37, 3) = -0.28706677187926227e-1, (37, 4) = 0.27971094145282712e-4, (37, 5) = -0.1315582904251911e-3, (38, 1) = .9561612871284315, (38, 2) = 0.16032468497041725e-1, (38, 3) = -0.22716201697191084e-1, (38, 4) = 0.9108284297335907e-5, (38, 5) = -0.4337758039619726e-4, (39, 1) = .958858965635045, (39, 2) = 0.12038500162795706e-1, (39, 3) = -0.18782005182342264e-1, (39, 4) = 0.3608857075468415e-5, (39, 5) = -0.17441599450102097e-4, (40, 1) = .9606217197165348, (40, 2) = 0.914514325386327e-2, (40, 3) = -0.1593723322791538e-1, (40, 4) = 0.15973572885621025e-5, (40, 5) = -0.7881196067433009e-5, (41, 1) = .9618157889669987, (41, 2) = 0.693594504796013e-2, (41, 3) = -0.13768928625667299e-1, (41, 4) = 0.7578240406846033e-6, (41, 5) = -0.3856388483481057e-5, (42, 1) = .9625579336916471, (42, 2) = 0.53653148882890234e-2, (42, 3) = -0.12229837199143657e-1, (42, 4) = 0.40466831691457055e-6, (42, 5) = -0.21455723871656463e-5, (43, 1) = .9630321047416508, (43, 2) = 0.4208610204678467e-2, (43, 3) = -0.11097927826763769e-1, (43, 4) = 0.23599512230457527e-6, (43, 5) = -0.13185086023573497e-5, (44, 1) = .9633548330674003, (44, 2) = 0.3291032013106795e-2, (44, 3) = -0.10201119562353245e-1, (44, 4) = 0.14351096807189318e-6, (44, 5) = -0.8585799100739333e-6, (45, 1) = .9635794225798572, (45, 2) = 0.25318181431538732e-2, (45, 3) = -0.9459930001639555e-2, (45, 4) = 0.8857046151520711e-7, (45, 5) = -0.5807183930298681e-6, (46, 1) = .9637351936467563, (46, 2) = 0.18861028334058306e-2, (46, 3) = -0.8830217058260243e-2, (46, 4) = 0.54176953171370387e-7, (46, 5) = -0.40321204700634103e-6, (47, 1) = .9638401434562422, (47, 2) = 0.1326072836040432e-2, (47, 3) = -0.828462376949864e-2, (47, 4) = 0.318508859340672e-7, (47, 5) = -0.28512654551555526e-6, (48, 1) = .9639061617395365, (48, 2) = 0.8331693356556849e-3, (48, 3) = -0.7804900784463723e-2, (48, 4) = 0.16983012204335007e-7, (48, 5) = -0.20411108581207533e-6, (49, 1) = .963941530746681, (49, 2) = 0.39433359612162176e-3, (49, 3) = -0.7378210574196815e-2, (49, 4) = 0.69058956940428584e-8, (49, 5) = -0.14716673870893628e-6, (50, 1) = .963952255758426, (50, 2) = .0, (50, 3) = -0.6995152048687603e-2, (50, 4) = .0, (50, 5) = -0.10635754806174274e-6}, datatype = float[8], order = C_order); YP := Matrix(50, 5, {(1, 1) = 1.0, (1, 2) = -1.016912631477338, (1, 3) = 1.0441113000581643, (1, 4) = 4.938383111325546, (1, 5) = -6.300000001197, (2, 1) = .9467292622483128, (2, 2) = -.9622772113928727, (2, 3) = .9858658256476173, (2, 4) = 4.513346170739063, (2, 5) = -9.397726517168355, (3, 1) = .895783706943777, (3, 2) = -.9101344320647631, (3, 3) = .9306188716382228, (3, 4) = 3.9305405877166715, (3, 5) = -11.898421382065955, (4, 1) = .8470745536097423, (4, 2) = -.860373451742725, (4, 3) = .8781815609789202, (4, 4) = 3.223524805389885, (4, 5) = -13.658581076246108, (5, 1) = .8005166268083528, (5, 2) = -.8128903023040563, (5, 3) = .8283850614020614, (5, 4) = 2.4329926016781056, (5, 5) = -14.605204201259696, (6, 1) = .75602811722521, (6, 2) = -.7675871163117387, (6, 3) = .7810774091586878, (6, 4) = 1.6030729437227047, (6, 5) = -14.737398181156987, (7, 1) = .7135303716905912, (7, 2) = -.7243714778269336, (7, 3) = .736120927464283, (7, 4) = .7775670166921098, (7, 5) = -14.11984902259275, (8, 1) = .6729477074610013, (8, 2) = -.6831558741457402, (8, 3) = .6933901181953316, (8, 4) = -0.34653255090257517e-2, (8, 5) = -12.86986662367746, (9, 1) = .6342072469341395, (9, 2) = -.6438572302054374, (9, 3) = .6527699319356851, (9, 4) = -.7064433677651218, (9, 5) = -11.140371532431427, (10, 1) = .5972387696518396, (10, 2) = -.6063965109971585, (10, 3) = .6141543418494605, (10, 4) = -1.3061198107940517, (10, 5) = -9.101399121783686, (11, 1) = .5619745789945647, (11, 2) = -.5706983801552904, (11, 3) = .5774451625788978, (11, 4) = -1.786473233829117, (11, 5) = -6.922501599763635, (12, 1) = .528349381415236, (12, 2) = -.5366909051394194, (12, 3) = .5425510675586522, (12, 4) = -2.1406810006817762, (12, 5) = -4.757927035769672, (13, 1) = .49630017642071433, (13, 2) = -.5043053012120328, (13, 3) = .5093867676411815, (13, 4) = -2.3703112091517946, (13, 5) = -2.7357798403575755, (14, 1) = .46569879325333513, (14, 2) = -.4734077198356524, (14, 3) = .47780288184693964, (14, 4) = -2.4840706437151705, (14, 5) = -.9479420024892491, (15, 1) = .4362259970506212, (15, 2) = -.44367242988215233, (15, 3) = .44745677095276526, (15, 4) = -2.4948251356156317, (15, 5) = .5549628621234142, (16, 1) = .4078186772916242, (16, 2) = -.41503308219069956, (16, 3) = .4182730703373508, (16, 4) = -2.4170112399060972, (16, 5) = 1.7348439985152488, (17, 1) = .3804427617884565, (17, 2) = -.3874529846540737, (17, 3) = .39020778707321313, (17, 4) = -2.267713799142949, (17, 5) = 2.5800100903859544, (18, 1) = .35406397565685854, (18, 2) = -.3608955340280772, (18, 3) = .36321791869790376, (18, 4) = -2.0653717123140347, (18, 5) = 3.10352774783306, (19, 1) = .32864756458000216, (19, 2) = -.33532390992055233, (19, 3) = .3372610306662744, (19, 4) = -1.8284211343980543, (19, 5) = 3.338204225824109, (20, 1) = .30415792526822016, (20, 2) = -.310700681058048, (20, 3) = .31229476274132867, (20, 4) = -1.5741295655423746, (20, 5) = 3.3306826139938144, (21, 1) = .2805580974006707, (21, 2) = -.2869872780487047, (21, 3) = .28827621621397953, (21, 4) = -1.3176869854655087, (21, 5) = 3.135340081336959, (22, 1) = .25780904339388555, (22, 2) = -.2641432592769831, (22, 3) = .2651611467004155, (22, 4) = -1.071588245625372, (22, 5) = 2.8085890119139396, (23, 1) = .2358685927532746, (23, 2) = -.2421252475321414, (23, 3) = .2429028386476426, (23, 4) = -.845310470542935, (23, 5) = 2.4040407789305567, (24, 1) = .2147861043754655, (24, 2) = -.2209818389817886, (24, 3) = .2215478846918326, (24, 4) = -.6461214157898081, (24, 5) = 1.9708474985101825, (25, 1) = .1946582172929835, (25, 2) = -.20080896597698863, (25, 3) = .20119072468789445, (25, 4) = -.47835610933187955, (25, 5) = 1.5502363494870965, (26, 1) = .1754386620756086, (26, 2) = -.18155930417548316, (26, 3) = .18178134653653813, (26, 4) = -.3421381651798363, (26, 5) = 1.1691948647879093, (27, 1) = .15707596816855374, (27, 2) = -.16318052643948905, (27, 3) = .163265092403284, (27, 4) = -.23553722921336775, (27, 5) = .843584392498727, (28, 1) = .13951234873701424, (28, 2) = -.14561421333147123, (28, 3) = .14558155088667368, (28, 4) = -.15525672367643156, (28, 5) = .579846478687003, (29, 1) = .12267930610986412, (29, 2) = -.12879150739256892, (29, 3) = .12866019319975472, (29, 4) = -0.9724838130607329e-1, (29, 5) = .3771503810083066, (30, 1) = .10651370141941992, (30, 2) = -.1126492397968819, (30, 3) = .11243661620708013, (30, 4) = -0.5727653723318041e-1, (30, 5) = .22984451471051648, (31, 1) = 0.9131052167272624e-1, (31, 2) = -0.9748175032923309e-1, (31, 3) = 0.9720567649632728e-1, (31, 4) = -0.3172088613075896e-1, (31, 5) = .13122010765127654, (32, 1) = 0.7712276927556598e-1, (32, 2) = -0.8334133909913169e-1, (32, 3) = 0.8301865455597775e-1, (32, 4) = -0.1640104680740198e-1, (32, 5) = 0.6969808445659362e-1, (33, 1) = 0.6385549523046109e-1, (33, 2) = -0.7013295494960084e-1, (33, 3) = 0.697791531221788e-1, (33, 4) = -0.7780056793655609e-2, (33, 5) = 0.3386354889433578e-1, (34, 1) = 0.51386320628059305e-1, (34, 2) = -0.57734884774429875e-1, (34, 3) = 0.5736461661467379e-1, (34, 4) = -0.32884474837452868e-2, (34, 5) = 0.14622944136188972e-1, (35, 1) = 0.4010243173621042e-1, (35, 2) = -0.4653193161278045e-1, (35, 3) = 0.4615955076341791e-1, (35, 4) = -0.12396732969434932e-2, (35, 5) = 0.5614885492478633e-2, (36, 1) = 0.30399509190318585e-1, (36, 2) = -0.36915005251636664e-1, (36, 3) = 0.3655279612231743e-1, (36, 4) = -0.42674003103921183e-3, (36, 5) = 0.19621942697003233e-2, (37, 1) = 0.22101471191290013e-1, (37, 2) = -0.28706677187926227e-1, (37, 3) = 0.2836431384167678e-1, (37, 4) = -0.1315582904251911e-3, (37, 5) = 0.6125409350740502e-3, (38, 1) = 0.16032468497041725e-1, (38, 2) = -0.22716201697191084e-1, (38, 3) = 0.22396703157973173e-1, (38, 4) = -0.4337758039619726e-4, (38, 5) = 0.20391637652164134e-3, (39, 1) = 0.12038500162795706e-1, (39, 2) = -0.18782005182342264e-1, (39, 3) = 0.18482442781990245e-1, (39, 4) = -0.17441599450102097e-4, (39, 5) = 0.8262561468904556e-4, (40, 1) = 0.914514325386327e-2, (40, 2) = -0.1593723322791538e-1, (40, 3) = 0.15655099226423174e-1, (40, 4) = -0.7881196067433009e-5, (40, 5) = 0.3763299224344935e-4, (41, 1) = 0.693594504796013e-2, (41, 2) = -0.13768928625667299e-1, (41, 3) = 0.13502115795304808e-1, (41, 4) = -0.3856388483481057e-5, (41, 5) = 0.18593261137575973e-4, (42, 1) = 0.53653148882890234e-2, (42, 2) = -0.12229837199143657e-1, (42, 3) = 0.11975148890593406e-1, (42, 4) = -0.21455723871656463e-5, (42, 5) = 0.10461587263954827e-4, (43, 1) = 0.4208610204678467e-2, (43, 2) = -0.11097927826763769e-1, (43, 3) = 0.1085291089737409e-1, (43, 4) = -0.13185086023573497e-5, (43, 5) = 0.6512757251742076e-5, (44, 1) = 0.3291032013106795e-2, (44, 2) = -0.10201119562353245e-1, (44, 3) = 0.9964270993547896e-2, (44, 4) = -0.8585799100739333e-6, (44, 5) = 0.4306718669414423e-5, (45, 1) = 0.25318181431538732e-2, (45, 2) = -0.9459930001639555e-2, (45, 3) = 0.9230202345693167e-2, (45, 4) = -0.5807183930298681e-6, (45, 5) = 0.29672863441924835e-5, (46, 1) = 0.18861028334058306e-2, (46, 2) = -0.8830217058260243e-2, (46, 3) = 0.8606824708215374e-2, (46, 4) = -0.40321204700634103e-6, (46, 5) = 0.2106799928695533e-5, (47, 1) = 0.1326072836040432e-2, (47, 2) = -0.828462376949864e-2, (47, 3) = 0.8066948681837108e-2, (47, 4) = -0.28512654551555526e-6, (47, 5) = 0.15306828052634482e-5, (48, 1) = 0.8331693356556849e-3, (48, 2) = -0.7804900784463723e-2, (48, 3) = 0.75924401275222035e-2, (48, 4) = -0.20411108581207533e-6, (48, 5) = 0.11324938030775855e-5, (49, 1) = 0.39433359612162176e-3, (49, 2) = -0.7378210574196815e-2, (49, 3) = 0.7170544922301032e-2, (49, 4) = -0.14716673870893628e-6, (49, 5) = 0.85021168502143e-6, (50, 1) = .0, (50, 2) = -0.6995152048687603e-2, (50, 3) = 0.6791924748889848e-2, (50, 4) = -0.10635754806174274e-6, (50, 5) = 0.6458986698603491e-6}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(50, {(1) = .0, (2) = 0.538450712436539e-1, (3) = .1082766859915131, (4) = .16331444031270473, (5) = .2189790463606035, (6) = .2752924234461127, (7) = .33227779889470094, (8) = .38995982000331736, (9) = .4483646786278111, (10) = .5075202501873479, (11) = .5674562491788733, (12) = .6282044036635384, (13) = .6897986516330131, (14) = .7524176453724036, (15) = .816715733668989, (16) = .8829036702135253, (17) = .9511585880378444, (18) = 1.0216871515791115, (19) = 1.0947329467114486, (20) = 1.170586433436612, (21) = 1.2495986390793312, (22) = 1.3322004686809672, (23) = 1.4189307352844525, (24) = 1.5100425310518173, (25) = 1.605556044446249, (26) = 1.706170701849191, (27) = 1.8128032039007311, (28) = 1.9266829029680352, (29) = 2.049525210932362, (30) = 2.1836360719075385, (31) = 2.3285917464945434, (32) = 2.485839068288575, (33) = 2.6591632259916818, (34) = 2.8548144648261875, (35) = 3.0721020019341, (36) = 3.305701178649673, (37) = 3.559949463816246, (38) = 3.7970789219278824, (39) = 3.990153302379728, (40) = 4.15720355507037, (41) = 4.306208343595448, (42) = 4.427174986030093, (43) = 4.526423733667591, (44) = 4.612636841962476, (45) = 4.689904237648306, (46) = 4.7605405732587975, (47) = 4.826006890793816, (48) = 4.88729546673539, (49) = 4.945116721690995, (50) = 5.0}, datatype = float[8], order = C_order); Y := Matrix(50, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.15143863606013115e-13, (1, 4) = .0, (1, 5) = 0.5209145281927147e-8, (2, 1) = -0.8264612893080438e-16, (2, 2) = 0.10601022236424583e-14, (2, 3) = 0.13448281300622448e-13, (2, 4) = 0.2531723244828144e-9, (2, 5) = 0.5151764399789821e-8, (3, 1) = -0.9818312986936232e-16, (3, 2) = 0.2024546298845675e-14, (3, 3) = 0.11603414280085763e-13, (3, 4) = 0.5031439996715309e-9, (3, 5) = 0.49505227176451794e-8, (4, 1) = -0.16400920960349306e-15, (4, 2) = 0.22923225644852182e-14, (4, 3) = 0.9858996413953448e-14, (4, 4) = 0.7435382816273587e-9, (4, 5) = 0.4613790921382858e-8, (5, 1) = 0.16695611005256184e-15, (5, 2) = 0.2920750522546946e-14, (5, 3) = 0.8715810892933721e-14, (5, 4) = 0.968257325936286e-9, (5, 5) = 0.4156299767076735e-8, (6, 1) = 0.3785488577501235e-15, (6, 2) = 0.34710943442817573e-14, (6, 3) = 0.7739663648523766e-14, (6, 4) = 0.11717218646887862e-8, (6, 5) = 0.359812314472648e-8, (7, 1) = 0.5735291564092602e-15, (7, 2) = 0.5559621333708256e-14, (7, 3) = 0.64794162714847054e-14, (7, 4) = 0.1349065434755046e-8, (7, 5) = 0.29635492365957813e-8, (8, 1) = 0.7392908645452232e-15, (8, 2) = 0.3999400361865862e-14, (8, 3) = 0.6347742731734012e-14, (8, 4) = 0.14963058193845247e-8, (8, 5) = 0.2279713504762398e-8, (9, 1) = 0.6831780723045333e-15, (9, 2) = 0.5442883341070182e-14, (9, 3) = 0.56555333890748366e-14, (9, 4) = 0.1610546333661808e-8, (9, 5) = 0.15751280801152935e-8, (10, 1) = 0.12805951228799598e-14, (10, 2) = 0.5552725838454675e-14, (10, 3) = 0.494213125294359e-14, (10, 4) = 0.16900532451603174e-8, (10, 5) = 0.8780983197662242e-9, (11, 1) = 0.1589045835010457e-14, (11, 2) = 0.54573811395900386e-14, (11, 3) = 0.4370346233896689e-14, (11, 4) = 0.1734384141772804e-8, (11, 5) = 0.21511245732875356e-9, (12, 1) = 0.1938397406295573e-14, (12, 2) = 0.65363028178274735e-14, (12, 3) = 0.39915199224484734e-14, (12, 4) = 0.17443804487181745e-8, (12, 5) = -0.3906337574991102e-9, (13, 1) = 0.25746355641282846e-14, (13, 2) = 0.6686301295711723e-14, (13, 3) = 0.3776993739734716e-14, (13, 4) = 0.17221022298538633e-8, (13, 5) = -0.9204760276081012e-9, (14, 1) = 0.24021854692179305e-14, (14, 2) = 0.68388696506603025e-14, (14, 3) = 0.3589227807197002e-14, (14, 4) = 0.16706007423685053e-8, (14, 5) = -0.13619565204084925e-8, (15, 1) = 0.27844846589144917e-14, (15, 2) = 0.6806482863864933e-14, (15, 3) = 0.3255802330557269e-14, (15, 4) = 0.15931710762978012e-8, (15, 5) = -0.1710057839046858e-8, (16, 1) = 0.3170168392339236e-14, (16, 2) = 0.7058625852330826e-14, (16, 3) = 0.3059882244808441e-14, (16, 4) = 0.14936064638531152e-8, (16, 5) = -0.19605804146242323e-8, (17, 1) = 0.418450905753915e-14, (17, 2) = 0.7320624596592493e-14, (17, 3) = 0.25290623286820664e-14, (17, 4) = 0.1376224007726725e-8, (17, 5) = -0.2113726736115561e-8, (18, 1) = 0.522802446903785e-14, (18, 2) = 0.7583088387046541e-14, (18, 3) = 0.2656436255857598e-14, (18, 4) = 0.12456454647509306e-8, (18, 5) = -0.2174149264673966e-8, (19, 1) = 0.5599963613653709e-14, (19, 2) = 0.7792902420006349e-14, (19, 3) = 0.2298977816983502e-14, (19, 4) = 0.1106554758169108e-8, (19, 5) = -0.21502682643665226e-8, (20, 1) = 0.5865892702136685e-14, (20, 2) = 0.8092855141368515e-14, (20, 3) = 0.2509193086994891e-14, (20, 4) = 0.9634933725685698e-9, (20, 5) = -0.205341703724594e-8, (21, 1) = 0.6816420131570755e-14, (21, 2) = 0.7846294298633722e-14, (21, 3) = 0.22775440990284527e-14, (21, 4) = 0.8206611972083126e-9, (21, 5) = -0.1896857216112942e-8, (22, 1) = 0.7301012092886368e-14, (22, 2) = 0.7949612920729695e-14, (22, 3) = 0.19113297564801313e-14, (22, 4) = 0.6817767801598973e-9, (22, 5) = -0.16947933473596584e-8, (23, 1) = 0.7517850272435388e-14, (23, 2) = 0.844440889491318e-14, (23, 3) = 0.210172135546369e-14, (23, 4) = 0.5499764453689152e-9, (23, 5) = -0.14614844738189918e-8, (24, 1) = 0.9093082110941868e-14, (24, 2) = 0.8617808603338214e-14, (24, 3) = 0.1973966157355317e-14, (24, 4) = 0.4281530842561462e-9, (24, 5) = -0.12106705564003452e-8, (25, 1) = 0.9614190502196018e-14, (25, 2) = 0.8848373195710656e-14, (25, 3) = 0.2086102522252812e-14, (25, 4) = 0.3188261735784484e-9, (25, 5) = -0.9556847653193206e-9, (26, 1) = 0.1041568490829814e-13, (26, 2) = 0.893833612887857e-14, (26, 3) = 0.1856000845238865e-14, (26, 4) = 0.22345041334248272e-9, (26, 5) = -0.708864527271831e-9, (27, 1) = 0.1152901561368169e-13, (27, 2) = 0.89795369925252e-14, (27, 3) = 0.2071787429729606e-14, (27, 4) = 0.14287136200501294e-9, (27, 5) = -0.4806758343384607e-9, (28, 1) = 0.13495965110034514e-13, (28, 2) = 0.9150624849596765e-14, (28, 3) = 0.18643959445317172e-14, (28, 4) = 0.7730346102119082e-10, (28, 5) = -0.27925524569939634e-9, (29, 1) = 0.1447846668412635e-13, (29, 2) = 0.9061416074595552e-14, (29, 3) = 0.2277139811068211e-14, (29, 4) = 0.26236748156626518e-10, (29, 5) = -0.10967840766932284e-9, (30, 1) = 0.1637043045937391e-13, (30, 2) = 0.8735733718415329e-14, (30, 3) = 0.27774780827091533e-14, (30, 4) = -0.11566251997979936e-10, (30, 5) = 0.26584437011128173e-10, (31, 1) = 0.19157667101419045e-13, (31, 2) = 0.8123059896172982e-14, (31, 3) = 0.36940270461759766e-14, (31, 4) = -0.3338327910770145e-10, (31, 5) = 0.11387033083646781e-9, (32, 1) = 0.218389656225817e-13, (32, 2) = 0.6857924190366744e-14, (32, 3) = 0.5214825473490382e-14, (32, 4) = -0.40398750655901706e-10, (32, 5) = 0.14926462934637388e-9, (33, 1) = 0.2627628563699054e-13, (33, 2) = 0.401556619991872e-14, (33, 3) = 0.8152745438393999e-14, (33, 4) = -0.3804768632584147e-10, (33, 5) = 0.14874007073963709e-9, (34, 1) = 0.36370999494014086e-13, (34, 2) = -0.386548921701265e-14, (34, 3) = 0.1631808180318328e-13, (34, 4) = -0.33000222761584506e-10, (34, 5) = 0.13693032069292921e-9, (35, 1) = 0.5509262327612127e-13, (35, 2) = -0.18890089391438668e-13, (35, 3) = 0.3161707194631968e-13, (35, 4) = -0.16646067039944626e-10, (35, 5) = 0.7219686567800556e-10, (36, 1) = 0.7409383620236018e-13, (36, 2) = -0.36040651044841214e-13, (36, 3) = 0.4898335208487011e-13, (36, 4) = 0.32784502413364445e-11, (36, 5) = -0.14735420939556755e-10, (37, 1) = 0.10169362342003957e-12, (37, 2) = -0.6040877776984526e-13, (37, 3) = 0.7350859063809685e-13, (37, 4) = 0.6987192987396587e-11, (37, 5) = -0.31593308676975374e-10, (38, 1) = 0.9107063627312493e-13, (38, 2) = -0.46451392159979334e-13, (38, 3) = 0.5970703758877559e-13, (38, 4) = 0.31960324368762172e-11, (38, 5) = -0.14549863332219355e-10, (39, 1) = 0.7795348303548032e-13, (39, 2) = -0.307504836025312e-13, (39, 3) = 0.4400477767345146e-13, (39, 4) = -0.24540000756116013e-12, (39, 5) = 0.14204634414083795e-11, (40, 1) = 0.7037299697401581e-13, (40, 2) = -0.2113986584686098e-13, (40, 3) = 0.3446868361893824e-13, (40, 4) = -0.6711604095422506e-12, (40, 5) = 0.33730077034860774e-11, (41, 1) = 0.6567420110784044e-13, (41, 2) = -0.1487071052735246e-13, (41, 3) = 0.281975245609803e-13, (41, 4) = -0.4840307488210744e-12, (41, 5) = 0.24565250659311624e-11, (42, 1) = 0.6459712022715409e-13, (42, 2) = -0.11097162630862281e-13, (42, 3) = 0.24423024403583574e-13, (42, 4) = -0.28608148225793283e-12, (42, 5) = 0.14964581624333766e-11, (43, 1) = 0.640280502136775e-13, (43, 2) = -0.8548606846495986e-14, (43, 3) = 0.21881466472077222e-13, (43, 4) = -0.16940774104908874e-12, (43, 5) = 0.9262688645940507e-12, (44, 1) = 0.6244301847516393e-13, (44, 2) = -0.66219479488107194e-14, (44, 3) = 0.1995701245760364e-13, (44, 4) = -0.10237686507119983e-12, (44, 5) = 0.5948441235731513e-12, (45, 1) = 0.6185753483413617e-13, (45, 2) = -0.5051468771290501e-14, (45, 3) = 0.18395260491368303e-13, (45, 4) = -0.6239441019233403e-13, (45, 5) = 0.3942092903383439e-12, (46, 1) = 0.6165132946892792e-13, (46, 2) = -0.37441003592832135e-14, (46, 3) = 0.1709672398590452e-13, (46, 4) = -0.3763161671814335e-13, (46, 5) = 0.26764102662748244e-12, (47, 1) = 0.6198151724876583e-13, (47, 2) = -0.26188562204839776e-14, (47, 3) = 0.15967252338380992e-13, (47, 4) = -0.21819149987483318e-13, (47, 5) = 0.18495665706484231e-12, (48, 1) = 0.6094944363926368e-13, (48, 2) = -0.1640899643671393e-14, (48, 3) = 0.15000579561151843e-13, (48, 4) = -0.11483823318682457e-13, (48, 5) = 0.1293625847432827e-12, (49, 1) = 0.6143323589996598e-13, (49, 2) = -0.7734412660573863e-15, (49, 3) = 0.14134062292410381e-13, (49, 4) = -0.4614422689930712e-14, (49, 5) = 0.9108760894060782e-13, (50, 1) = 0.6135526225959751e-13, (50, 2) = .0, (50, 3) = 0.13373226403332908e-13, (50, 4) = .0, (50, 5) = 0.6421709636688081e-13}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[50] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(5.209145281927147e-9) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 50, [y(x), diff(y(x), x), diff(diff(y(x), x), x), z(x), diff(z(x), x)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[50] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[50] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(50, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(50, 5, X, Y, outpoint, yout, L, V) end if; [x = outpoint, seq('[y(x), diff(y(x), x), diff(diff(y(x), x), x), z(x), diff(z(x), x)]'[i] = yout[i], i = 1 .. 5)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[50] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(5.209145281927147e-9) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 50, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[50] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[50] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(50, 5, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(50, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(0..0, {}), (3) = [x, y(x), diff(y(x), x), diff(diff(y(x), x), x), z(x), diff(z(x), x)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [x = res[1], seq('[y(x), diff(y(x), x), diff(diff(y(x), x), x), z(x), diff(z(x), x)]'[i] = res[i+1], i = 1 .. 5)] catch: error  end try end proc

(5)

print(sol(0));

[x = 0., y(x) = HFloat(0.0), diff(y(x), x) = HFloat(0.9999999999999998), diff(diff(y(x), x), x) = HFloat(-1.0169126314773378), z(x) = HFloat(0.9999999999999998), diff(z(x), x) = HFloat(4.938383111325545)]

(6)

odeplot(sol, [x, diff(y(x), x)], x = 0 .. 5)

 

odeplot(sol, [x, z(x)], x = 0 .. 5)

 
 

 

Download Code.mw


The Summer Issue of Maple Transactions has been published.  There are articles from a range of interests: research, education, and personal stories.

Have a look, and I hope you find something of value in the issue.

 

Could anyone help me with the syntax to create a Region Plot (Feasibility or Preference Map) that displays: Regions based on conditions like:

  • When   and  πR>πD ​ ​, then Strategy 1 is preferred.
    and  When ​, πR<πD then Strategy 2 is better.
     
  • When ​,πR<πD then Strategy 2 is preferred.
    and When ​,πR>πD then Strategy 1 is better.

I’d also like the plot to visually highlight the regions based on strategy​, and vice versa.

File : Regional_plot.mw

Hello everyone,
Could someone tell me how to insert an entry (empty cell) between two already filled entries or above an already filled entry in Document Mode?

Oliveira

As the following worksheet shows, Student:-NumericalAnalysis:-MatrixDecomposition cannot factorize the input matrix  and throws an error, but if we simply reorder or exchange the elements of , no error will be raised. (The reason for setting  is that LinearAlgebra:-LUDecomposition can be used for other methods.) 
 

restart

with(Student:-NumericalAnalysis, MatrixDecomposition)

m := Matrix([[3*(sqrt(3)+1)/8,-1/2,1/2,-(sqrt(3)+1)/8,-1/2,1/2,-(sqrt(3)+1)/8,-1/2,1/2,-(sqrt(3)+1)/8],

             [-1/2,sqrt(3)-1,-(sqrt(3)-1),-1/2,0,0,1/2,0,0,1/2],

             [1/2,-(sqrt(3)-1),sqrt(3)-1,1/2,0,0,-1/2,0,0,-1/2],

             [-(sqrt(3)+1)/8,-1/2,1/2,3*(sqrt(3)+1)/8,1/2,-1/2,-(sqrt(3)+1)/8,1/2,-1/2,-(sqrt(3)+1)/8],

             [-1/2,0,0,1/2,sqrt(3)-1,-(sqrt(3)-1),-1/2,0,0,1/2],

             [1/2,0,0,-1/2,-(sqrt(3)-1),sqrt(3)-1,1/2,0,0,-1/2],

             [-(sqrt(3)+1)/8,1/2,-1/2,-(sqrt(3)+1)/8,-1/2,1/2,3*(sqrt(3)+1)/8,1/2,-1/2,-(sqrt(3)+1)/8],

             [-1/2,0,0,1/2,0,0,1/2,sqrt(3)-1,-(sqrt(3)-1),-1/2],

             [1/2,0,0,-1/2,0,0,-1/2,-(sqrt(3)-1),sqrt(3)-1,1/2],

             [-(sqrt(3)+1)/8,1/2,-1/2,-(sqrt(3)+1)/8,1/2,-1/2,-(sqrt(3)+1)/8,-1/2,1/2,3*(sqrt(3)+1)/8]],

            'shape'='symmetric'):

MatrixDecomposition(m, 'method' = 'LDLt'): # this does not work 

Error, (in Student:-NumericalAnalysis:-MatrixDecomposition) a pivot element 0 is encountered, and the entries below it are not all 0; the factorization cannot continue

 

MatrixDecomposition(m([1, 4, 7, 10, 2, 5, 8, 3, 6, 9] $ 2), 'method' = 'LDLt'): # yet this works 

MatrixDecomposition(m([2, 3, 5, 6, 8, 9, 1, 4, 7, 10] $ 2), 'method' = 'LDLt'): # this also works 

randomize(5):

k := 0:
to 1e3 do
        try
                MatrixDecomposition(m(combinat:-randperm(10) $ 2), 'method' = 'LDLt')
        catch :
                k++
        end
od:
k/1e3;

.469

(1)


 

Download LDL_factorization_robustness.mw

The last instance above suggests that it only works on about half of the inputs (that are equivalent to each other). Although I tried changing the value of Digits, the failure rate remained high. Is Student:-NumericalAnalysis:-MatrixDecomposition not robust enough? 

I am learning how to use Maple for solving single and systems of linear PDE's using the Laplace transform (LT)method so the resulting solution in s space can be used to generate the moments of the resulting probability distribution.

When I take the LT of a term such as Uxx(t,x), I expect a second order ordinary derivative. Instead, it shows the Laplace transform operator.

Here is a simple test code  

with(inttrans):

with(DEtools):

rhs_pde := diff(u(x, t), x, x);

laplace_rhs_pde := laplace(rhs_pde, t, s);

I want to draw a circle in 2D as a point plot, given a center y1 and radius r1 using the animate command. 
I can do this for other functions, and I can create a plot of a circle, but I am doing something wrong when I attempt to combine them.  

Here is my code

with(plots):

y1:=<-1,1>;
r1:=15.;

This plot command for the circle works.  

plot([y1(1)+r1*cos(t),y1(2)+r1*sin(t),t=0..2*Pi],color=blue); [n];

But this attempt to animate it does not!!!

plots:-animate(plot,([[y1(1)+r1*cos(t),y1(2)+r1*sin(t)], t=0..T,color=blue]), T=0..2*Pi); plot([y1(1)+r1*cos(t),y1(2)+r1*sin(t),t=0..2*Pi],color=blue);

Thanks

I experience the following quirk using maple 2025 in worksheet mode: copy a formula and then paste it can often freeze the program. Termination only via ctrl-Alt-delete task manager. Has anybody similar problems or should i think that is happening only in my case?

I am working with two plots and need help in labeling,

Plot 1: I would like to display the intersection point of the two curves along with the corresponding value of δ (delta) at that point. Ideally, this can be highlighted using an arrow or annotation.

Plot 2: I would like to identify and mark the maximum point of the two curves. Specifically, I want to show the maximum value and the corresponding value of w at which this occurs.

Could anyone help with the syntax. Is there any method to improve the quality of figure to export it as jpeg?

Q_NEW_PLOT.mw

On maple I want solve this, is the best way plot angles by time?I put M,m,r,theta,phy and plot first and than the second equation?

We are pleased to announce that the registration for the Maple Conference 2025 is now open!

Like the last few years, this year’s conference will be a free virtual event. Please visit the conference page for more information on how to register.

This year we are offering a number of new sessions, including more product training options, and an Audience Choice session.
Also included in this year's registration is access to an in-depth Maple workshop day presented by Maplesoft's R&D members following the conference.  You can find an overview of the program on the Sessions page. Those who register before September 14th, 2025 will have a chance to vote for the topics they want to learn more about during the Audience Choice session.

We hope to see you there!

Greetings,

I have generated two random points in the unit square.  Each point has an x and y coordinate.  The density function for the (absolute) distance between each point is (2-2d) in both the x and y direction.  These distances are shown by the "f" and "g" functions attached.

The overall (rectilinear) difference is what I am after.  The attached worksheet shows the rectilinear distance as "h".  

My question is this...how can I obtain this rectilinear distance by using convolution and the "starting" density function of (2-2d) ? 

This is probably more of a mathematics function than a Maple question, but the "rules" of convolution, particularly setting the upper and lower boundaries of the integrals confuse me.

 

DensityFunction.mw

in here i did all steps but i know something is missing becuase in finding parameter all x and y and t must be remove but still one x is remain so something is wrong with my substitution for finding parameter where is mistake ?

n1.mw

f(a).b;            #ok
                           (f(a)) . b

op(0, f(a).b);     #ok
                               .

lprint(f(a).b);    #ok
f(a) . b

f(7).b;            #???
                             f(7) b

op(0, f(7).b);     #???
                               *

lprint(f(7).b);    #???
f(7)*b

 

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