Advanced Search

mehdibgh

240 Reputation

6 Badges

8 years, 15 days
Contact mehdibgh

MaplePrimes Activity


These are questions asked by mehdibgh

How to solve a set of equaions using fso...

mehdibgh 240 Maple 2016
matrix indexing fsolve
July 28 2022
2 9

I have a set of equations gathered in a vector. The number of equations varies each time. Here in this example it is 4. How you suggest so solve them with fsolve? I tried to use seq but faced error.

> 

restart
> 

EQ := Matrix(4, 1, {(1, 1) = 32.1640740637930*Tau[1]-0.172224519601111e-4*Tau[2]-0.270626540730518e-3*Tau[3]+0.1570620334e-9*P[1]+0.3715450960e-14*sin(t), (2, 1) = -0.172224519601111e-4*Tau[1]+32.1667045885952*Tau[2]+0.587369829416537e-4*Tau[3]-0.1589565489e-8*P[1]+0.1004220091e-12*sin(t), (3, 1) = -0.270626540730518e-3*Tau[1]+0.587369829416537e-4*Tau[2]+32.1816411689934*Tau[3]-0.7419658527e-8*P[1]+0.5201228088e-12*sin(t), (4, 1) = 0.1570620334e-9*Tau[1]-0.1589565489e-8*Tau[2]-0.7419658527e-8*Tau[3]+601.876235436204*P[1]})
> 

V := Matrix(1, 4, {(1, 1) = Tau[1], (1, 2) = Tau[2], (1, 3) = Tau[3], (1, 4) = P[1]})
> 

q := 0
> 

X := Matrix(4, 1, {(1, 1) = -0.1156532164e-15*sin(t), (2, 1) = -0.3121894613e-14*sin(t), (3, 1) = -0.1616209235e-13*sin(t), (4, 1) = -0.2074537757e-24*sin(t)})
> 

t := 1
> 

Xf := fsolve({seq(EQ[r], r = 1 .. 4)}, {seq(V[r] = q .. X[r], r = 1 .. 4)})

Error, Matrix index out of range``

``

Download SoalNewton.mw

Why GenerateMatrix produces wrong result...

mehdibgh 240 Maple 2016
linearalgebra generatematrix
June 22 2022
1 0

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...

mehdibgh 240 Maple 2016
integration numeric romberg
June 11 2022
2 3

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

How to speed up the calculation of the d...

mehdibgh 240 Maple 2016
performance integration legendrep
June 03 2022
0 1

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 th...

mehdibgh 240 Maple
generatematrix
February 24 2022
1 6

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)
> 

``
> 

``

``

Download GenMatrix.mw

1 2 3 4 5 6 7 Last Page 3 of 18