mehdibgh

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6 years, 17 days

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These are questions asked by mehdibgh

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)

``

``

``

Download GenMatrix.mw

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

I have a big matrix which is computed in a worksheet, now I have to use this matrix in another worksheet. Could you recommend some ways of healthy transferring of quantities between worksheets?

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