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mehdi jafari

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These are replies submitted by mehdi jafari

u can remove this part...

mehdi jafari 764
March 26 2014
0 0

@mehdi jafari 

u can laso solve without considering (parametric=full, parameters={seq(b[i],i=1..50)}) .  i also changed 

for x to 50 do fu[x] := fun(x*delt) = m(x*delt) end do:

 from 49 to 50 so that your equations equal to parameters.

why u do not enter your equations here ?...

mehdi jafari 764
March 26 2014
0 0

please uplaod your worksheet or write down your equations here. good luck

yessss, me tooo...

mehdi jafari 764
March 26 2014
0 0

@Alejandro Jakubi i have recieced emails too. tnx to mapleprimes good staff.

yesssss...

mehdi jafari 764
March 24 2014
0 0

@Markiyan Hirnyk  at first answer your question ?! :)

for adavnced users i mean, what is the best book for advanced maple users,

plot and animate...

mehdi jafari 764
March 23 2014
0 0

@ilke 

NULL

> 

restart:
> 

sys:={54.15836673*(diff(Y(t), t$2)) = -365.4395362*(diff(X(t), t))+208.2315661*Y(t),641.1196154*(diff(X(t), t$2)) = 365.4395362*(diff(Y(t), t))-2.575699975*X(t)-7.882173342};

{641.1196154*(diff(diff(X(t), t), t)) = 365.4395362*(diff(Y(t), t))-2.575699975*X(t)-7.882173342, 54.15836673*(diff(diff(Y(t), t), t)) = -365.4395362*(diff(X(t), t))+208.2315661*Y(t)}

 (1)
> 

BCs:={X(0) = 0, X(15) = 0, Y(0) = 0, Y(15) = 0};

{X(0) = 0, X(15) = 0, Y(0) = 0, Y(15) = 0}

 (2)
> 

ans:=dsolve(sys union BCs,method = bvp,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(39, {(1) = .0, (2) = .38351121101718294, (3) = .7670525174337857, (4) = 1.1505124184681526, (5) = 1.5339974108667955, (6) = 1.9176656846625835, (7) = 2.301666900840626, (8) = 2.686166017900895, (9) = 3.0714248709070704, (10) = 3.4578482205784917, (11) = 3.8459964328894594, (12) = 4.236562473720028, (13) = 4.63029143999511, (14) = 5.027875289828752, (15) = 5.429838794289437, (16) = 5.836424009646885, (17) = 6.2474993950021105, (18) = 6.662514723812331, (19) = 7.0804709956849745, (20) = 7.500000000010247, (21) = 7.919529004335479, (22) = 8.337485276208003, (23) = 8.752500605018055, (24) = 9.163575990373069, (25) = 9.570161205730289, (26) = 9.972124710190753, (27) = 10.369708560024193, (28) = 10.763437526299098, (29) = 11.154003567129536, (30) = 11.542151779440406, (31) = 11.928575129111765, (32) = 12.313833982117927, (33) = 12.698333099178127, (34) = 13.082334315356094, (35) = 13.46600258915182, (36) = 13.849487581545711, (37) = 14.232947482570854, (38) = 14.616488788987173, (39) = 15.0}, datatype = float[8], order = C_order); Y := Matrix(39, 4, {(1, 1) = .0, (1, 2) = -0.6793369507317244e-1, (1, 3) = .0, (1, 4) = -1.9459338300331779, (2, 1) = -.10602083366137158, (2, 2) = -.47830225714828567, (2, 3) = -.7117780496690446, (2, 4) = -1.7639009337730573, (3, 1) = -.36160003234017934, (3, 2) = -.8472923030359297, (3, 3) = -1.3514541665563253, (3, 4) = -1.5697893895641046, (4, 1) = -.7502210987400865, (4, 2) = -1.1720549705223295, (4, 3) = -1.914414678410873, (4, 4) = -1.3647080837605474, (5, 1) = -1.2545530420596849, (5, 2) = -1.4502553791819308, (5, 3) = -2.39689767195954, (5, 4) = -1.15018486564728, (6, 1) = -1.8566173481546144, (6, 2) = -1.6799591168281722, (6, 3) = -2.79579656195079, (6, 4) = -.9281704537475385, (7, 1) = -2.5378521768016573, (7, 2) = -1.8596637699845209, (7, 3) = -3.1087154929089165, (7, 4) = -.7010051571974785, (8, 1) = -3.279288032751613, (8, 2) = -1.9883866750492754, (8, 3) = -3.334122195861295, (8, 4) = -.4713409316902086, (9, 1) = -4.061886116890226, (9, 2) = -2.065729725471639, (9, 3) = -3.4714619352702867, (9, 4) = -.24202885448366737, (10, 1) = -4.866826172046525, (10, 2) = -2.091868276601214, (10, 3) = -3.5211409222552237, (10, 4) = -0.1603573298160153e-1, (11, 1) = -5.675665479260962, (11, 2) = -2.0675031801983383, (11, 3) = -3.484446320882544, (11, 4) = .20360220465223156, (12, 1) = -6.470336286978461, (12, 2) = -1.9938169734959315, (12, 3) = -3.3634729722172945, (12, 4) = .4137863074411373, (13, 1) = -7.232967882314578, (13, 2) = -1.872482432656078, (13, 3) = -3.161138803756909, (13, 4) = .6113217112064968, (14, 1) = -7.945694250521905, (14, 2) = -1.7057564611764606, (14, 3) = -2.8813454574345343, (14, 4) = .7928834016987208, (15, 1) = -8.590600279196805, (15, 2) = -1.4966558142118183, (15, 3) = -2.5292781992830395, (15, 4) = .9550156730871263, (16, 1) = -9.149934028828042, (16, 2) = -1.2491872517510594, (16, 3) = -2.111798389510939, (16, 4) = 1.0941915922740408, (17, 1) = -9.606698109768974, (17, 2) = -.9685705146665443, (17, 3) = -1.6378237999177483, (17, 4) = 1.2069567468244398, (18, 1) = -9.945624169660137, (18, 2) = -.6613721970818361, (18, 3) = -1.1185574549472468, (18, 4) = 1.2901567914192125, (19, 1) = -10.154386401967724, (19, 2) = -.3355082255048767, (19, 3) = -.5674927431143325, (19, 4) = 1.3412154143317405, (20, 1) = -10.224912267171778, (20, 2) = 0.822899012356365e-11, (20, 3) = 0.13919232841285866e-10, (20, 4) = 1.358433178318087, (21, 1) = -10.154386401960862, (21, 2) = .3355082255210961, (21, 3) = .5674927431417645, (21, 4) = 1.3412154143300643, (22, 1) = -9.945624169646688, (22, 2) = .6613721970973515, (22, 3) = 1.1185574549734794, (22, 4) = 1.2901567914159184, (23, 1) = -9.606698109749443, (23, 2) = .968570514680947, (23, 3) = 1.6378237999420855, (23, 4) = 1.2069567468196336, (24, 1) = -9.149934028803116, (24, 2) = 1.2491872517639921, (24, 3) = 2.111798389532771, (24, 4) = 1.0941915922678662, (25, 1) = -8.590600279167282, (25, 2) = 1.4966558142229935, (25, 3) = 2.529278199301876, (25, 4) = .9550156730797464, (26, 1) = -7.945694250488633, (26, 2) = 1.705756461185658, (26, 3) = 2.8813454574499993, (26, 4) = .792883401690306, (27, 1) = -7.232967882278435, (27, 2) = 1.8724824326631273, (27, 3) = 3.1611388037687087, (27, 4) = .6113217111972187, (28, 1) = -6.47033628694033, (28, 2) = 1.9938169735007036, (28, 3) = 3.363472972225207, (28, 4) = .41378630743116585, (29, 1) = -5.675665479221692, (29, 2) = 2.0675031802007426, (29, 3) = 3.48444632088641, (29, 4) = .20360220464171913, (30, 1) = -4.866826172006997, (30, 2) = 2.0918682766011796, (30, 3) = 3.52114092225492, (30, 4) = -0.16035732992500905e-1, (31, 1) = -4.061886116851318, (31, 2) = 2.0657297254691165, (31, 3) = 3.471461935265727, (31, 4) = -.24202885449480616, (32, 1) = -3.2792880327141893, (32, 2) = 1.988386675044235, (32, 3) = 3.334122195852423, (32, 4) = -.4713409317014557, (33, 1) = -2.537852176766784, (33, 2) = 1.8596637699769885, (33, 3) = 3.108715492895771, (33, 4) = -.7010051572086486, (34, 1) = -1.8566173481232375, (34, 2) = 1.6799591168182009, (34, 3) = 2.795796561933454, (34, 4) = -.928170453758488, (35, 1) = -1.254553042032688, (35, 2) = 1.4502553791695916, (35, 3) = 2.3968976719381296, (35, 4) = -1.1501848656578912, (36, 1) = -.7502210987238381, (36, 2) = 1.1720549705114174, (36, 3) = 1.9144146783919551, (36, 4) = -1.3647080837681445, (37, 1) = -.36160003233624866, (37, 2) = .8472923030317289, (37, 3) = 1.3514541665490432, (37, 4) = -1.5697893895665231, (38, 1) = -.1060208336592883, (38, 2) = .47830225714385494, (38, 3) = .711778049661362, (38, 4) = -1.7639009337751965, (39, 1) = .0, (39, 2) = 0.6793369507317255e-1, (39, 3) = .0, (39, 4) = -1.9459338300331794}, datatype = float[8], order = C_order); YP := Matrix(39, 4, {(1, 1) = -0.6793369507317244e-1, (1, 2) = -1.1214807851677133, (1, 3) = -1.9459338300331779, (1, 4) = .4583900792957371, (2, 1) = -.47830225714828567, (2, 2) = -1.0172957104381275, (2, 3) = -1.7639009337730573, (2, 4) = .4907071357964794, (3, 1) = -.8472923030359297, (3, 2) = -.9056249296622738, (3, 3) = -1.5697893895641046, (3, 4) = .5210402443184181, (4, 1) = -1.1720549705223295, (4, 2) = -.7871668654837667, (4, 3) = -1.3647080837605474, (4, 4) = .5479053370681317, (5, 1) = -1.4502553791819308, (5, 2) = -.662862022532546, (5, 3) = -1.15018486564728, (5, 4) = .5700115972869568, (6, 1) = -1.6799591168281722, (6, 2) = -.5338945432253852, (6, 3) = -.9281704537475385, (6, 4) = .586250764446552, (7, 1) = -1.8596637699845209, (7, 2) = -.4016729809663424, (7, 3) = -.7010051571974785, (7, 4) = .5956968773479954, (8, 1) = -1.9883866750492754, (8, 2) = -.2677851661110939, (8, 3) = -.4713409316902086, (8, 4) = .5976106713973248, (9, 1) = -2.065729725471639, (9, 2) = -.1339327071567271, (9, 3) = -.24202885448366737, (9, 4) = .5914387616732935, (10, 1) = -2.091868276601214, (10, 2) = -0.18823010351991486e-2, (10, 3) = -0.1603573298160153e-1, (10, 4) = .5768025510882371, (11, 1) = -2.0675031801983383, (11, 2) = .12656130210245609, (11, 3) = .20360220465223156, (11, 4) = .5534821429233556, (12, 1) = -1.9938169734959315, (12, 2) = .24955927740252992, (12, 3) = .4137863074411373, (12, 4) = .5214024577770111, (13, 1) = -1.872482432656078, (13, 2) = .3652187498862573, (13, 3) = .6113217112064968, (13, 4) = .48063170177329617, (14, 1) = -1.7057564611764606, (14, 2) = .47157267763404304, (14, 3) = .7928834016987208, (14, 4) = .43139729604922294, (15, 1) = -1.4966558142118183, (15, 2) = .5665793269987861, (15, 3) = .9550156730871263, (15, 4) = .37411848400665626, (16, 1) = -1.2491872517510594, (16, 2) = .6481570201882005, (16, 3) = 1.0941915922740408, (16, 4) = .3094503210388524, (17, 1) = -.9685705146665443, (17, 2) = .71426844774737, (17, 3) = 1.2069567468244398, (17, 4) = .23832596112727966, (18, 1) = -.6613721970818361, (18, 2) = .7630542855243145, (18, 3) = 1.2901567914192125, (18, 4) = .16198011259091505, (19, 1) = -.3355082255048767, (19, 2) = .792996511423492, (19, 3) = 1.3412154143317405, (19, 4) = 0.8194611356782522e-1, (20, 1) = 0.822899012356365e-11, (20, 2) = .8030940111712972, (20, 3) = 1.358433178318087, (20, 4) = -0.2008455706211582e-11, (21, 1) = .3355082255210961, (21, 2) = .7929965114225089, (21, 3) = 1.3412154143300643, (21, 4) = -0.8194611357179582e-1, (22, 1) = .6613721970973515, (22, 2) = .763054285522383, (22, 3) = 1.2901567914159184, (22, 4) = -.16198011259474576, (23, 1) = .968570514680947, (23, 2) = .7142684477445519, (23, 3) = 1.2069567468196336, (23, 4) = -.2383259611308901, (24, 1) = 1.2491872517639921, (24, 2) = .6481570201845809, (24, 3) = 1.0941915922678662, (24, 4) = -.30945032104217596, (25, 1) = 1.4966558142229935, (25, 2) = .566579326994461, (25, 3) = .9550156730797464, (25, 4) = -.37411848400963876, (26, 1) = 1.705756461185658, (26, 2) = .4715726776291129, (26, 3) = .792883401690306, (26, 4) = -.43139729605182175, (27, 1) = 1.8724824326631273, (27, 2) = .36521874988082353, (27, 3) = .6113217111972187, (27, 4) = -.48063170177549175, (28, 1) = 1.9938169735007036, (28, 2) = .24955927739669304, (28, 3) = .41378630743116585, (28, 4) = -.521402457778791, (29, 1) = 2.0675031802007426, (29, 2) = .1265613020963062, (29, 3) = .20360220464171913, (29, 4) = -.5534821429247145, (30, 1) = 2.0918682766011796, (30, 2) = -0.1882301041570623e-2, (30, 3) = -0.16035732992500905e-1, (30, 4) = -.5768025510891714, (31, 1) = 2.0657297254691165, (31, 2) = -.13393270716323252, (31, 3) = -.24202885449480616, (31, 4) = -.5914387616738033, (32, 1) = 1.988386675044235, (32, 2) = -.26778516611765507, (32, 3) = -.4713409317014557, (32, 4) = -.5976106713974243, (33, 1) = 1.8596637699769885, (33, 2) = -.40167298097284954, (33, 3) = -.7010051572086486, (33, 4) = -.5956968773477129, (34, 1) = 1.6799591168182009, (34, 2) = -.5338945432317524, (34, 3) = -.928170453758488, (34, 4) = -.5862507644459232, (35, 1) = 1.4502553791695916, (35, 2) = -.662862022538703, (35, 3) = -1.1501848656578912, (35, 4) = -.5700115972860171, (36, 1) = 1.1720549705114174, (36, 2) = -.7871668654881623, (36, 3) = -1.3647080837681445, (36, 4) = -.5479053370672382, (37, 1) = .8472923030317289, (37, 2) = -.9056249296636681, (37, 3) = -1.5697893895665231, (37, 4) = -.5210402443180708, (38, 1) = .47830225714385494, (38, 2) = -1.0172957104393552, (38, 3) = -1.7639009337751965, (38, 4) = -.4907071357961206, (39, 1) = 0.6793369507317255e-1, (39, 2) = -1.1214807851677142, (39, 3) = -1.9459338300331794, (39, 4) = -.45839007929573783}, 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(39, {(1) = .0, (2) = .38351121101718294, (3) = .7670525174337857, (4) = 1.1505124184681526, (5) = 1.5339974108667955, (6) = 1.9176656846625835, (7) = 2.301666900840626, (8) = 2.686166017900895, (9) = 3.0714248709070704, (10) = 3.4578482205784917, (11) = 3.8459964328894594, (12) = 4.236562473720028, (13) = 4.63029143999511, (14) = 5.027875289828752, (15) = 5.429838794289437, (16) = 5.836424009646885, (17) = 6.2474993950021105, (18) = 6.662514723812331, (19) = 7.0804709956849745, (20) = 7.500000000010247, (21) = 7.919529004335479, (22) = 8.337485276208003, (23) = 8.752500605018055, (24) = 9.163575990373069, (25) = 9.570161205730289, (26) = 9.972124710190753, (27) = 10.369708560024193, (28) = 10.763437526299098, (29) = 11.154003567129536, (30) = 11.542151779440406, (31) = 11.928575129111765, (32) = 12.313833982117927, (33) = 12.698333099178127, (34) = 13.082334315356094, (35) = 13.46600258915182, (36) = 13.849487581545711, (37) = 14.232947482570854, (38) = 14.616488788987173, (39) = 15.0}, datatype = float[8], order = C_order); Y := Matrix(39, 4, {(1, 1) = .0, (1, 2) = 0.4169474949470319e-8, (1, 3) = .0, (1, 4) = 0.7835240842428686e-7, (2, 1) = -0.23769322024608386e-8, (2, 2) = 0.20574993513536933e-7, (2, 3) = 0.28915467105198323e-7, (2, 4) = 0.6739578827522519e-7, (3, 1) = 0.13432614554121212e-8, (3, 2) = 0.3455328846284316e-7, (3, 3) = 0.53555371547114894e-7, (3, 4) = 0.56808022185555136e-7, (4, 1) = 0.10215180140437365e-7, (4, 2) = 0.46210741231203555e-7, (4, 3) = 0.7412236554868284e-7, (4, 4) = 0.4655270349628992e-7, (5, 1) = 0.23345917507038193e-7, (5, 2) = 0.5565120904080144e-7, (5, 3) = 0.9081227975256859e-7, (5, 4) = 0.36610408987452024e-7, (6, 1) = 0.39899737408272976e-7, (6, 2) = 0.6297121533476722e-7, (6, 3) = 0.10380568393478045e-6, (6, 4) = 0.26980586305072067e-7, (7, 1) = 0.59092586147958576e-7, (7, 2) = 0.6826227696538385e-7, (7, 3) = 0.11327212034532727e-6, (7, 4) = 0.17679640490096123e-7, (8, 1) = 0.8018750204181922e-7, (8, 2) = 0.7161521879446997e-7, (8, 3) = 0.119377899946789e-6, (8, 4) = 0.8737080945867287e-8, (9, 1) = 0.10249438427814322e-6, (9, 2) = 0.7312342317943269e-7, (9, 3) = 0.12229202004119914e-6, (9, 4) = 0.19111174725149373e-9, (10, 1) = 0.12537059509966982e-6, (10, 2) = 0.7288351861281618e-7, (10, 3) = 0.12218760188581384e-6, (10, 4) = -0.7914095997972168e-8, (11, 1) = 0.14821970623535092e-6, (11, 2) = 0.7099509769899028e-7, (11, 3) = 0.11924158176630196e-6, (11, 4) = -0.15529823095629243e-7, (12, 1) = 0.17048746533454583e-6, (12, 2) = 0.6756068395918315e-7, (12, 3) = 0.11363480905133206e-6, (12, 4) = -0.2260318036205843e-7, (13, 1) = 0.1916550626721734e-6, (13, 2) = 0.6268707361085955e-7, (13, 3) = 0.10555443975346679e-6, (13, 4) = -0.29076602733567843e-7, (14, 1) = 0.21123297474510157e-6, (14, 2) = 0.5648861648180569e-7, (14, 3) = 0.9519964592930939e-7, (14, 4) = -0.3488759907336914e-7, (15, 1) = 0.22875849192160096e-6, (15, 2) = 0.4909200331686155e-7, (15, 3) = 0.8278991187863618e-7, (15, 4) = -0.3996949062688898e-7, (16, 1) = 0.243799139386567e-6, (16, 2) = 0.4064167014273389e-7, (16, 3) = 0.68574371853428e-7, (16, 4) = -0.44253446873786724e-7, (17, 1) = 0.2559630838180394e-6, (17, 2) = 0.3130438765940954e-7, (17, 3) = 0.5283974357116317e-7, (17, 4) = -0.4767211588664755e-7, (18, 1) = 0.2649153933065295e-6, (18, 2) = 0.2127148944881124e-7, (18, 3) = 0.359142760601206e-7, (18, 4) = -0.5016454130276307e-7, (19, 1) = 0.27039685011429327e-6, (19, 2) = 0.10758443348014332e-7, (19, 3) = 0.18167086595288972e-7, (19, 4) = -0.5168150189899868e-7, (20, 1) = 0.2722428369590898e-6, (20, 2) = -0.16362472803880316e-15, (20, 3) = 0.6585452897692007e-16, (20, 4) = -0.52190877518771335e-7, (21, 1) = 0.27039684789364484e-6, (21, 2) = -0.10758443759892585e-7, (21, 3) = -0.18167086098998353e-7, (21, 4) = -0.51681501153762164e-7, (22, 1) = 0.26491539334159847e-6, (22, 2) = -0.21271489368459295e-7, (22, 3) = -0.3591427510772471e-7, (22, 4) = -0.50164540061434875e-7, (23, 1) = 0.2559630826316772e-6, (23, 2) = -0.3130438687584957e-7, (23, 3) = -0.528397420405275e-7, (23, 4) = -0.47672114560932285e-7, (24, 1) = 0.24379913797799355e-6, (24, 2) = -0.4064167016755145e-7, (24, 3) = -0.6857437093143762e-7, (24, 4) = -0.44253445979182944e-7, (25, 1) = 0.22875848980850263e-6, (25, 2) = -0.4909200134059814e-7, (25, 3) = -0.8278990964437361e-7, (25, 4) = -0.39969488578280374e-7, (26, 1) = 0.211232972263855e-6, (26, 2) = -0.56488614358634603e-7, (26, 3) = -0.9519964517538756e-7, (26, 4) = -0.34887596117693075e-7, (27, 1) = 0.19165506550982305e-6, (27, 2) = -0.6268707119103872e-7, (27, 3) = -0.1055544358184001e-6, (27, 4) = -0.2907660029411003e-7, (28, 1) = 0.1704874678186134e-6, (28, 2) = -0.6756068148678297e-7, (28, 3) = -0.11363480469247379e-6, (28, 4) = -0.2260318184630453e-7, (29, 1) = 0.14821970985770134e-6, (29, 2) = -0.7099509679967245e-7, (29, 3) = -0.11924157775958776e-6, (29, 4) = -0.15529825250558246e-7, (30, 1) = 0.1253706027608365e-6, (30, 2) = -0.728835199418429e-7, (30, 3) = -0.1221875992965587e-6, (30, 4) = -0.7914098566907212e-8, (31, 1) = 0.10249438939377254e-6, (31, 2) = -0.731234230669166e-7, (31, 3) = -0.12229201766964834e-6, (31, 4) = 0.19110773857564476e-9, (32, 1) = 0.8018750758996192e-7, (32, 2) = -0.7161521851463498e-7, (32, 3) = -0.11937789774462777e-6, (32, 4) = 0.8737076425495856e-8, (33, 1) = 0.5909258802411502e-7, (33, 2) = -0.6826227739932252e-7, (33, 3) = -0.11327212139868922e-6, (33, 4) = 0.17679637485508423e-7, (34, 1) = 0.3989974032995724e-7, (34, 2) = -0.6297121687044666e-7, (34, 3) = -0.10380568609432601e-6, (34, 4) = 0.26980584439462847e-7, (35, 1) = 0.23345918977407193e-7, (35, 2) = -0.55651210067980086e-7, (35, 3) = -0.9081228185305163e-7, (35, 4) = 0.36610409724641004e-7, (36, 1) = 0.1021518123179639e-7, (36, 2) = -0.4621074260181786e-7, (36, 3) = -0.7412236942890131e-7, (36, 4) = 0.4655270703828583e-7, (37, 1) = 0.1343261922182429e-8, (37, 2) = -0.3455328945578425e-7, (37, 3) = -0.5355537272993128e-7, (37, 4) = 0.5680802529503699e-7, (38, 1) = -0.23769320272060756e-8, (38, 2) = -0.20574994249066573e-7, (38, 3) = -0.28915468392130814e-7, (38, 4) = 0.6739579196183749e-7, (39, 1) = .0, (39, 2) = -0.41694749416285906e-8, (39, 3) = .0, (39, 4) = 0.7835241170249775e-7}, 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[39] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(2.722428369590898e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [4, 39, [X(t), diff(X(t), t), Y(t), diff(Y(t), t)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[39] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[39] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(4, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(39, 4, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(4, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(39, 4, X, Y, outpoint, yout, L, V) end if; [t = outpoint, seq('[X(t), diff(X(t), t), Y(t), diff(Y(t), t)]'[i] = yout[i], i = 1 .. 4)] 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[39] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(2.722428369590898e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [4, 39, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[39] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[39] 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(4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(39, 4, 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(4, {(1) = 0., (2) = 0., (3) = 0., (4) = 0.}); `dsolve/numeric/hermite`(39, 4, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 4)] end proc, (2) = Array(0..0, {}), (3) = [t, X(t), diff(X(t), t), Y(t), diff(Y(t), t)], (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); [t = res[1], seq('[X(t), diff(X(t), t), Y(t), diff(Y(t), t)]'[i] = res[i+1], i = 1 .. 4)] catch: error end try end proc

 (3)
> 

ans(1,1);

[t = 1., X(t) = HFloat(-0.5829077966809866), diff(X(t), t) = HFloat(-1.0500088098537468), Y(t) = HFloat(-1.702840309010038), diff(Y(t), t) = HFloat(-1.446427441705165)]

 (4)
> 

plots:-odeplot(ans,[X(t),Y(t)],t=0..15);

 
> 

plots:-odeplot(ans,[t,Y(t)],t=0..15);

 
> 

plots:-odeplot(ans,[t,X(t)],t=0..15);

 
> 

T(x)=-6.643572696*10^(-10)*cos(10733.58723*x)-0.8085449658e-4*cos(323.6693795*x)+0.8085516082e-4;

T(x) = -0.6643572696e-9*cos(10733.58723*x)-0.8085449658e-4*cos(323.6693795*x)+0.8085516082e-4

 (5)
> 

p := proc (x, T) options operator, arrow; plots:-odeplot(ans, [t, X(t)*T(x)], 0 .. 15) end proc; plots:-animate(p, [x, 7], x = 1e4 .. 1e6);

proc (x, T) options operator, arrow; plots:-odeplot(ans, [t, X(t)*T(x)], 0 .. 15) end proc

  

 
> 

``

NULL

your part of time answer is too small that choosing range 1e4..1e6 does not affect your results !

you may also see the link  http://www.mapleprimes.com/questions/150659-How-To-Plot-With-The-Results-Of-Desolve-Command  and see Preben Alsholm answer on this topic. good luck !

Download ode.mw

nice try...

mehdi jafari 764
March 23 2014
0 0

@Carl Love these system of equations are linear, so it seems that using fsolve is due to the complex part and when u use "convert_to_exact= false" option, it does count for the complex part and gives the answer. am i wrong ?

yes it is right...

mehdi jafari 764
March 23 2014
0 3

@ilke as i concluded X(t) is your displacement in y direction  and Y(t) is displacement in x direction, since you have maximum of X(t) in the middle which was expected and two extermum for displacement Y(t) in 1/4 and 3/4 . yes sould use numeric method. good luck

your boundary conditions are not correct...

mehdi jafari 764
March 23 2014
0 0

what is your beams supports at both end ?! is it clapmed at both end or simply supported ?! tel me your beam specifications so that i can tell your boundary conditions.

mine also does not work !...

mehdi jafari 764
March 23 2014
0 0


``

> 

restart
> 

for x from 0 to 5 do print(evalf(sum((-1)^k*x^(2*k)/factorial(2*k), k = 0 .. 10)), evalf(cos(x))) end do:

0., 1.

  

.5403023059, .5403023059

  

-.4161468365, -.4161468365

  

-.9899924966, -.9899924966

  

-.6536436057, -.6536436209

  

.2836642141, .2836621855

 (1)
> 

for x from 0 to 5 do print(evalf(add((-1)^k*x^(2*k)/factorial(2*k), k = 0 .. 10)), evalf(cos(x))) end do:

1., 1.

  

.5403023059, .5403023059

  

-.4161468365, -.4161468365

  

-.9899924966, -.9899924966

  

-.6536436057, -.6536436209

  

.2836642141, .2836621855

 (2)
> 

``

``

 

Download maple_18.mw

maybe...

mehdi jafari 764
March 23 2014
0 0

@Alejandro Jakubi  actually it is a good point to maple primes to check the issue. but i think it is somewaht that they know about,since i send an email ( contact part in the below of this page ) to mapleprimes staff, and it was so interesting that no one answered me !!! now i do not know whether they know what the problem and how to fix ! but they do know how to fix or not !!! , is the problem ! and i think they do !

i have encountered the problem too...

mehdi jafari 764
March 22 2014

 i have encountered the problem too, even in my own codes, not downloaded from mapleprimes, i plot in a worksheet and save it and close it , and after opening the file again,there was unwanted gridlines there ! actually you are right .

as @Markiyan Hirnyk says,...

mehdi jafari 764
March 21 2014
0 0


> 

int(exp(10*(y^4-2*y^2))*exp(-10*(z^4-2*z^2)), [z = -infinity .. y, y = -1 .. 0], numeric);

1276.267563

  

1276.267563

  

1276.267563

 (1)
> 

``


Download int.mw

make n global...

mehdi jafari 764
March 21 2014
0 0

@sarra  

NULL

> 

restart:
> 

ode := diff(y(x), x) = 2*x+y(x);
> 

f:=(x,y)->2*x-y;
> 

 

> 

analyticsol := rhs(dsolve({ode, y(0) = 1}));
> 

RKadaptivestepsize := proc (f, a, b, epsilon, N)
> 

global n;
local x, y,k,z,R,p,h,hstar;
> 

p:=2;

> 

h := evalf(b-a)/N; ## we begin with this setpsize
> 

x[0] := a; y[0] := 1;z[0]:=1; ## Initialisation
> 

for n from 0 to N-1 do  ##loop
> 

x[n+1] := a+(n+1)*h;  ## noeuds
> 

k[1] := f(x[n], y[n]);
> 

k[2] := f(x[n]+h, y[n]+h*k[1]);
> 

k[3] := f(x[n]+h/2, y[n]+h/4*(k[1]+k[2]));
> 

z[n+1] := z[n]+(h/2)*(k[1]+k[2]);## 2-stage runge Kutta.

> 

y[n+1] := y[n]+(h/6)*(k[1]+k[2]+4*k[3]);
> 

R:=abs(y[n+1]-z[n+1]); ## local erreur
> 

hstar:=sqrt(epsilon/R);
> 

if R<=epsilon then

> 

   x[n] := x[n+1]+h;

> 

   y[n]:=y[n+1];
   n:=n+1;
> 

else
> 

 

> 

h:=hstar;
> 

end if;
> 

 end do;
> 

[seq([x[i], y[i]], i = 0 .. N)];
> 

[seq([x[i], z[i]], i = 0 .. N)];
> 

end proc:
> 

epsilon:=1e-8;
> 

ans:=RKadaptivestepsize((x,y)->2*x-y,0,1, epsilon,20);

diff(y(x), x) = 2*x+y(x)

  

proc (x, y) options operator, arrow; 2*x-y end proc

  

-2*x-2+3*exp(x)

  

0.1e-7

  

[[0, 1], [0.5000000000e-1, .9537500000], [0.2529822128e-1, .9431799074], [0.3765843990e-1, .9322041622], [0.4983821056e-1, .9217502798], [0.6185717430e-1, .9117968125], [0.7372782360e-1, .9023241793], [0.8546135836e-1, .8933142925], [0.9706758048e-1, .8847504074], [.1085552954, .8766169594], [.1199324443, .8688994360], [.1312061689, .8615842706], [.1423828190, .8546587533], [.1534683349, .8481109364], [.1644679459, .8419295761], [.1753866618, .8361040561], [.1862287757, .8306243489], [.1969984958, .8254809504], [.2076995128, .8206648486], [.2183352831, .8161674787], [.2289090802, .8119806881]]

 (1)
> 

 

> 

plots:-pointplot(ans);

 
> 

 

> 

printf("%a is the number of steps required using 3-step Runge Kutta Method to achieve an eroor of 10^(-6) .", n);

20  is the number of steps required using 3-step Runge Kutta Method to achieve an  eroor of 10^(-6) .

  
> 

``

NULL

 

Download corrected.mw

this question is answered...

mehdi jafari 764
March 21 2014
0 2

@sarra  go to this link :

http://www.mapleprimes.com/questions/201190-How-Can-I-Use--If-When-I-Solve-This-Ode#answer204566

to see your answer. good luck !

your questions are so vague...

mehdi jafari 764
March 20 2014
0 0

could u tell me what does it mean?> Y'(t)  , it is differentiation with respect to what ?! how can u differentiate from a matrix ? please cleafy your differentiation . tnx

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