mehdibgh

215 Reputation

6 Badges

5 years, 165 days

MaplePrimes Activity


These are questions asked by mehdibgh

Why GenerateMatrix produces wrong results?

``

restart

N := 2:

a := 1:

with(ArrayTools):

``

Qa := [-0.5379667864e-1*(diff(tau[1, 1](t), t, t))+7.862351349*10^(-11)*tau[2, 1](t)-8.050993899*10^(-12)*(diff(tau[2, 1](t), t, t))+.1166068042*(diff(tau[1, 2](t), t))+2.181309895*10^(-11)*(diff(tau[2, 2](t), t))+.5309519363*tau[1, 1](t) = 0, -1.265965258*10^(-11)*(diff(tau[1, 1](t), t, t))+.4884414390*tau[2, 1](t)-0.4948946475e-1*(diff(tau[2, 1](t), t, t))+2.738892495*10^(-11)*(diff(tau[1, 2](t), t))+.1340883970*(diff(tau[2, 2](t), t))+1.246469610*10^(-10)*tau[1, 1](t) = 0, 3.649366137*10^(-10)*tau[2, 2](t)-9.135908950*10^(-12)*(diff(tau[2, 2](t), t, t))-5.160677740*10^(-11)*(diff(tau[2, 1](t), t))+1.953765755*tau[1, 2](t)-0.4948946473e-1*(diff(tau[1, 2](t), t, t))-.3476543209*(diff(tau[1, 1](t), t)) = 0, 2.246672656*tau[2, 2](t)-0.5690888318e-1*(diff(tau[2, 2](t), t, t))-.3198194887*(diff(tau[2, 1](t), t))+4.602903411*10^(-10)*tau[1, 2](t)-1.159417294*10^(-11)*(diff(tau[1, 2](t), t, t))-8.175817372*10^(-11)*(diff(tau[1, 1](t), t)) = 0]

Q1 := [seq(seq(diff(tau[i, j](t), t), i = 1 .. M), j = 1 .. N)]

[diff(tau[1, 1](t), t), diff(tau[2, 1](t), t), diff(tau[1, 2](t), t), diff(tau[2, 2](t), t)]

(1)

with(LinearAlgebra):

CR := GenerateMatrix(simplify(Qa), Q1)

CR := Matrix(4, 4, {(1, 1) = 0, (1, 2) = 0, (1, 3) = .1166068042, (1, 4) = 0.2181309895e-10, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0.2738892495e-10, (2, 4) = .1340883970, (3, 1) = -.3476543209, (3, 2) = -0.5160677740e-10, (3, 3) = 0, (3, 4) = 0, (4, 1) = -0.8175817372e-10, (4, 2) = -.3198194887, (4, 3) = 0, (4, 4) = 0}), Vector(4, {(1) = 0.5379667864e-1*(diff(diff(tau[1, 1](t), t), t))-0.7862351349e-10*tau[2, 1](t)+0.8050993899e-11*(diff(diff(tau[2, 1](t), t), t))-.5309519363*tau[1, 1](t), (2) = 0.1265965258e-10*(diff(diff(tau[1, 1](t), t), t))-.4884414390*tau[2, 1](t)+0.4948946475e-1*(diff(diff(tau[2, 1](t), t), t))-0.1246469610e-9*tau[1, 1](t), (3) = -0.3649366137e-9*tau[2, 2](t)+0.9135908950e-11*(diff(diff(tau[2, 2](t), t), t))-1.953765755*tau[1, 2](t)+0.4948946473e-1*(diff(diff(tau[1, 2](t), t), t)), (4) = -2.246672656*tau[2, 2](t)+0.5690888318e-1*(diff(diff(tau[2, 2](t), t), t))-0.4602903411e-9*tau[1, 2](t)+0.1159417294e-10*(diff(diff(tau[1, 2](t), t), t))})

(2)

``

``

``

Download GenMatrix.mw

Do you know why increasing the number of applications of trapezoidal rule results infinity and imaginary part?

I want get result for Romberg Integration Method with 6 Applications of Trapezoidal Rule.

restart

with(Student[NumericalAnalysis]):

``

fff := (eta__1^2-1.)^2*(zeta__1^2-1.)^2*(-5.6584306313*10^(-8)*eta__1^4*zeta__1^4-1.0454641424*10^(-8)*eta__1*zeta__1^4+5.6161016651*10^(-9)*eta__1^3*zeta__1^4+1.0615594865*10^(-8)*eta__1^5*zeta__1^4+5.4851856568*10^(-9)*eta__1^3*zeta__1^2-1.4132765167*10^(-8)*eta__1^5*zeta__1^2-7.8157365683*10^(-7)*zeta__1*eta__1^4+2.9373057668*10^(-8)*eta__1^5*zeta__1^5-7.032574429*10^(-8)*eta__1^3*zeta__1^5-5.2577413654*10^(-8)*eta__1^5*zeta__1^3+2.3272955826*10^(-8)*eta__1^5*zeta__1+1.5782217112*10^(-7)*eta__1^3*zeta__1^3+2.1771522925*10^(-8)*eta__1*zeta__1^5-8.3051507888*10^(-8)*eta__1^3*zeta__1-2.2997952126*10^(-8)*eta__1*zeta__1^3+0.22608138853e-5*eta__1^4-0.53519692056e-5*eta__1^2+0.62041471332e-4+0.54946587424e-4*zeta__1^2-0.10412827312e-5*zeta__1^4-0.53422910417e-5*zeta__1^3+0.12053033309e-3*zeta__1-4.5961086182*10^(-8)*eta__1^2*zeta__1^4-1.6404108106*10^(-7)*zeta__1^2*eta__1-1.5606093643*10^(-7)*zeta__1*eta__1^2-4.168658171*10^(-7)*zeta__1*eta__1-0.5430102455e-5*eta__1^2*zeta__1^5+0.87015148204e-5*eta__1^2*zeta__1^3+0.25592467903e-5*eta__1^4*zeta__1^5-0.4071733639e-5*eta__1^4*zeta__1^3-0.44664222239e-5*eta__1^4*zeta__1^2+0.84495460425e-5*eta__1^2*zeta__1^2+7.5007400675*10^(-7)*zeta__1^5-6.6427826628*10^(-9)*eta__1^3+3.5821686059*10^(-9)*eta__1^5-2.4361928132*10^(-7)*eta__1)/(-0.32350168299e-2*eta__1^5-0.40854298828e-3*zeta__1^8-0.57170204466e-1*eta__1^8+.26989142602*zeta__1^7+.34307133883*eta__1^6+.14111119517*eta__1^4-0.48267577378e-1*zeta__1^9-1.082755589*eta__1^2-1.3163499567*zeta__1^2+0.75042415188e-3*eta__1^7-0.40463518464e-2*zeta__1^6+.66506159208*zeta__1^4+.58641863992*zeta__1^3-0.18089939414e-3*eta__1^9-.60151130424*zeta__1^5+0.49423587807e-2*eta__1^3-0.22768667085e-2*eta__1-.20653118433*zeta__1-.15635457174*eta__1^8*zeta__1+.64029273264*eta__1^8*zeta__1^3-1.8403657443*eta__1^6*zeta__1^7-0.48478855017e-1*eta__1^8*zeta__1^4-0.22007436935e-2*eta__1^2*zeta__1^8+0.56271163518e-2*eta__1^4*zeta__1^8-.22701198791*eta__1^6*zeta__1^6-0.18753531811e-2*eta__1*zeta__1^9+0.63616448215e-2*eta__1^3*zeta__1^9-0.70972300998e-2*eta__1^5*zeta__1^9+0.26109384594e-2*eta__1^7*zeta__1^9+0.37597513815e-2*eta__1^9*zeta__1^7-.81152175007*eta__1^8*zeta__1^5+.32758358916*eta__1^8*zeta__1^7+.60516338422*eta__1^6*zeta__1-2.7777061884*eta__1^6*zeta__1^3+3.8764153863*eta__1^6*zeta__1^5+0.14976271107e-3*eta__1*zeta__1^8+0.64408301026e-3*eta__1^3*zeta__1^8-0.17374541537e-2*eta__1^5*zeta__1^8+0.9436084324e-3*eta__1^7*zeta__1^8-0.95617026598e-3*eta__1*zeta__1^6-0.79980551762e-3*eta__1^3*zeta__1^6-0.43427014208e-2*eta__1^7*zeta__1^6+0.52833995188e-2*eta__1^5*zeta__1^6-0.39563328597e-2*eta__1^7*zeta__1^2-0.30978282387e-2*zeta__1*eta__1+3.4563944947*eta__1^2*zeta__1^5-2.669958003*eta__1^2*zeta__1^3-5.9197768267*eta__1^4*zeta__1^5+4.2209528188*eta__1^4*zeta__1^3+.1920464905*eta__1^4*zeta__1^2+1.9334990569*eta__1^2*zeta__1^2+0.66050016962e-2*eta__1^7*zeta__1^4+.80614880365*eta__1^6*zeta__1^4-.9191903249*eta__1^6*zeta__1^2-1.724981418*zeta__1^7*eta__1^2+2.9678721471*zeta__1^7*eta__1^4-.94779423754*zeta__1*eta__1^4+.46301464814*zeta__1^6*eta__1^4-.22761063366*zeta__1^6*eta__1^2-0.85894534062e-2*eta__1^5*zeta__1^4+0.8278524871e-2*eta__1^5*zeta__1^2+0.46097207851e-2*eta__1^3*zeta__1^4-0.93963570584e-2*eta__1^3*zeta__1^2-0.81381430978e-3*eta__1*zeta__1^4-.62093209055*eta__1^2*zeta__1^4-.80179945016*eta__1^4*zeta__1^4+.70551660939*zeta__1*eta__1^2+0.38970885732e-2*zeta__1^2*eta__1+0.10746052526e-1*eta__1*zeta__1^7-0.40389225121e-1*eta__1^3*zeta__1^7+0.52300044044e-1*eta__1^5*zeta__1^7+.10999473421*eta__1^8*zeta__1^2-0.45528793761e-1*eta__1^7*zeta__1^3+0.57167454208e-1*eta__1^7*zeta__1^5+0.11770764739e-2*eta__1^9*zeta__1^2-0.18114547653e-2*eta__1^9*zeta__1^4+0.81527768559e-3*eta__1^9*zeta__1^6+0.13191002642e-1*eta__1*zeta__1^3+0.14324735033e-1*eta__1^3*zeta__1-0.18963873748e-1*eta__1*zeta__1^5-0.56315405543e-1*eta__1^3*zeta__1^3-0.21374958034e-1*eta__1^5*zeta__1+0.7601825081e-1*eta__1^3*zeta__1^5+.65574325943+0.80855499912e-1*eta__1^5*zeta__1^3-.10468335582*eta__1^5*zeta__1^5-0.26416622831e-1*eta__1^7*zeta__1^7-0.20189726843e-2*eta__1^9*zeta__1+0.77976967502e-2*eta__1^9*zeta__1^3-0.95384754473e-2*eta__1^9*zeta__1^5+.13649316215*eta__1^6*zeta__1^9+.23302831691*eta__1^2*zeta__1^9-.32125390168*eta__1^4*zeta__1^9+0.12167023924e-1*eta__1^7*zeta__1-0.301782967e-2*eta__1^6*zeta__1^8-0.43456747248e-2*eta__1^8*zeta__1^6):

plot3d(sqrt(fff), zeta__1 = -1 .. 1, eta__1 = -1 .. 1, color = green)

 

``

Quadrature(Quadrature(sqrt(fff), zeta__1 = -1 .. 1, method = romberg[3]), eta__1 = -1 .. 1, method = romberg[3])

0.2745463666e-1+0.*I

(1)

Student:-NumericalAnalysis:-Quadrature(Student:-NumericalAnalysis:-Quadrature(sqrt(fff), zeta__1 = -1 .. 1, method = romberg[4]), eta__1 = -1 .. 1, method = romberg[4])

0.3314502549e-1+0.*I

(2)

Student:-NumericalAnalysis:-Quadrature(Student:-NumericalAnalysis:-Quadrature(sqrt(fff), zeta__1 = -1 .. 1, method = romberg[5]), eta__1 = -1 .. 1, method = romberg[5])

0.3621732017e-1+0.*I

(3)

Student:-NumericalAnalysis:-Quadrature(Student:-NumericalAnalysis:-Quadrature(sqrt(fff), zeta__1 = -1 .. 1, method = romberg[6]), eta__1 = -1 .. 1, method = romberg[6])

Float(undefined)+Float(undefined)*I

(4)

``

Download question.mw

I want to calculate the double integral of the following expression which includes sum of several Legendre polynomial terms, but the speed is so low. Any suggestion to speed up the calculation?

NULL

Restart:

NULL

II := 9:

JJ := 9:

M := 9:

NULL

`ΔP1` := add(add(add(add(add(add(add(-(LegendreP(i, zeta__1)*LegendreP(j, eta__1)*(diff(diff(tau[r](t), t), t))+LegendreP(m, zeta__1)*LegendreP(j, eta__1)*(diff(tau[r](t), t))+LegendreP(m, zeta__1)*LegendreP(j, eta__1)*tau[r](t))/sqrt(LegendreP(m, zeta__1)*LegendreP(j, eta__1)+LegendreP(i, zeta__1)*LegendreP(l, eta__1)), i = 1 .. II), j = 1 .. JJ), k = 1 .. II), m = 1 .. II), l = 1 .. JJ), n = 1 .. JJ), r = 1 .. M):

A := int(int(`ΔP1`, zeta__1 = -1 .. 1), eta__1 = -1 .. 1):

A

``

Download Soal.mw

Why GenerateMatrix could not give out the coefficient matrix of the equations in terms of third order vector?

NULL

restart

``

with(LinearAlgebra):

Var[4] := [tau[1](t)^3, tau[2](t)^3, tau[3](t)^3, tau[4](t)^3, tau[5](t)^3, p[1](t)^3]:

EqML := [-0.467902632940817e-5*(-0.398588153114250e-4*tau[1](t)+0.571232697467613e-4*tau[2](t)+0.238866882336809e-4*tau[3](t)+0.333476161338209e-4*tau[4](t)+0.364093457033576e-4*tau[5](t)-p[1](t))^3, 0.670570063557231e-5*(-0.398588153114250e-4*tau[1](t)+0.571232697467613e-4*tau[2](t)+0.238866882336809e-4*tau[3](t)+0.333476161338209e-4*tau[4](t)+0.364093457033576e-4*tau[5](t)-p[1](t))^3, 0.280405833175180e-5*(-0.398588153114250e-4*tau[1](t)+0.571232697467613e-4*tau[2](t)+0.238866882336809e-4*tau[3](t)+0.333476161338209e-4*tau[4](t)+0.364093457033576e-4*tau[5](t)-p[1](t))^3, 0.391467665794924e-5*(-0.398588153114250e-4*tau[1](t)+0.571232697467613e-4*tau[2](t)+0.238866882336809e-4*tau[3](t)+0.333476161338209e-4*tau[4](t)+0.364093457033576e-4*tau[5](t)-p[1](t))^3, 0.427409309211715e-5*(-0.398588153114250e-4*tau[1](t)+0.571232697467613e-4*tau[2](t)+0.238866882336809e-4*tau[3](t)+0.333476161338209e-4*tau[4](t)+0.364093457033576e-4*tau[5](t)-p[1](t))^3, -.11739000000*(-0.398588153114250e-4*tau[1](t)+0.571232697467613e-4*tau[2](t)+0.238866882336809e-4*tau[3](t)+0.333476161338209e-4*tau[4](t)+0.364093457033576e-4*tau[5](t)-p[1](t))^3]:

KKNL := GenerateMatrix(EqML, Var[4])[1]

KKNL := Matrix(6, 6, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0, (5, 6) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 0})

(1)

``

``

``

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I have two surfaces f=f(x,y) and g=g(x,y), is there any way to find the equation of intersection curve of them in maple?

contact.mw

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