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How do I solve the two dimensional P.D.E in Maple?...

Asked by: iqra naz 5
August 16 2016
1  3

i have an example, u[t] = u[xx]^2+u[yy]^2+u[zz]^2 with subject to b.c. u[0](x,y,z,t):=2*sin(x)*sin(y)*sin(z)
i used adomian method to solve this P.D.E, but i failed to construct a code of 2D P.D.E.
kindly help me in this regard

Does there exist a routine for minimizing an energ...

Asked by: alecjacobson 30
optimization physics calculus-of-variations
August 16 2016
3  6

Is there a maple routine or sequence of routines to minimize an energy functional (scalar energy with a function as an argument)?

I'd like to avoid applying calculus of variations/integration by parts by hand.

For example, I'm looking for something like:

E := int(diff(f(x),x)^2,x=0..1);
bc := f(0) = 0, f(1) = 1;
minimize(E,bc);

whose result would be:

       f(x) = x

Is there a way to use dsolve to do this?

Convert Maple online examples into raw text entry?...

Asked by: alecjacobson 30
August 16 2016
2  4

Maple's online help pages render all of the inputs (and outputs) as fancy math (MathJax). I guess the assumption is that you're using the visual IDE. However, I only have access to a terminal with ASCII entry (e.g., via SSH).

How can I can convert the online help pages into something that I can enter directly via the command line?

For example, how do I convert the examples from the EulerLagrange help page into command line entry?

I'm looking for a procedural way or ideally a toggle "switch".

word needed for definition...

Asked by: Adam Ledger 360
implicit multivariate
August 16 2016
0  3

what do i call a homogenous  differential equation that is the linear sum of "N" differential of unique classification? ie, the implicit construction of a third homogenous differential by the summation of two known, is it the span of the solution sets of the first two or union? i prefer span because well that leaves the door open for multivariate differential basis definitions, non commutative groups like sets of square matrices and all of the other extra arousing subject content.

Computing the Sine and Cosine Funtion...

Asked by: behappy 10
syntax pi
August 15 2016
1  12

Hi,

When I type sin(pi/2) the result is sin(pi/2) (not "1.0)

What should I do to get "1.0" instead of replicating the sin(pi/2) ?!

I mean why the expression contating "pi" can not being simplified?

Is there any solution to this problem?

 

Thanks

how do I plot a solution with series representatio...

Asked by: necron 70
August 15 2016
1  8

Hi! I'm trying to find the way to plot the solution with series representation. I need some help to find the easiest way.

Note: I realized some typing errors, which do not change the question a lot ,and I corrected them.

plot.mw

Why I am unable to see length of MapleSim rigid bo...

Asked by: onder 50
August 15 2016
0  5

Hi,

I am unable to see length of rigid body frame in MapleSim Examples - Physical Domain  - Multibody - 5 DOF robot? Is there a way to see them?

Thanks

Onder

How to sort a polynomial equation with many variab...

Asked by: Kabilan 0
polynomial sort power
August 15 2016
0  4

If an expression is of the form x^3 + x^2 + x + z + y^3 + y^2 + y + xy=0 ,

How to represent it in the following form,

           x^3 + y^3 + x^2 + y^2 + xy + x + y + z=0 ?

exporting to latex...

Asked by: Annonymouse 160
latex export
August 15 2016
1  3

I have exported a maple document to latex, but it only shows the output of the commands used. Rather than the commands, and the procedures.

How do I get both to export together? and show up together?

 

Automatically convert and paste as 2D math...

Asked by: Samuel Hollis 100
convert clipboard
August 15 2016
1  0

Is there a way to automatically convert and paste my clipboard contents as 2D math?

latex document preparation from maple worksheets...

Asked by: Adam Ledger 360
latex export rtfm
August 15 2016
0  1

any assistence here will be much appreciated the website gave me a zip containing the template tex and other files, but for what ever reason its not working when i copy in output using the maple to latex conversion feature from inside the interface. literally im sick of having to work outside of the maple interface but yes believe it or not this is the one thing i use to procrastinate writting a formal publication yep i really need the first one of those to get this done and dusted.

error after use ''for'' in program...

Asked by: torabi 90
dsolve numeric approximateint
August 14 2016
0  1

hi..when i use rule [for] in maple code i encounter error'''''

Error, (in dsolve/numeric/process_input) input system must be an ODE system, found {f1(x), f2(x), f3(x), ApproximateInt(-4*cos(theta)^2, theta = 0. .. 1, method = simpson), ApproximateInt(4*cos(theta)^2, theta = 0. .. 1, method = simpson), ApproximateInt(8*cos(theta)^2, theta = 0. .. 1, method = simpson)}''''''''

please help me for remove it

99999999999999.mw

i want for different beta for example beta=0, 40 and 80 this lines will computed three times  

 ''with(Student[Calculus1]); a1 := ApproximateInt(g1*g1, theta = a .. 1, method = simpson); a2 := ApproximateInt(2*(g1*g1)+3*g1*(diff(g1, theta, theta)), theta = a .. 1, method = simpson).......................''          

 by {for i from 1 by 1 to 3 do } and final gain ''ITRA_1_W[m] := eval(fy33*g3, fixedparameter)'' that have 3 amount.

when i use  rule {for i from 1 by 1 to 3 do ...  }   integral not computed and showed for example:::

a1=ApproximateInt(4*cos(theta)^2, theta = 0. .. 1, method = simpson)!!!!!!!!

thanks..

another problem with integral...

Asked by: mehdi jafari 774
integral numeric
August 14 2016
0  5

another problem with itegral, again intergal is getting unevaluated answers or folated ( infinity )
what should i do ?

``

``

> 

restart
> 

with(LinearAlgebra):
> 

Digits := 30;

30

 (1)

``

> 

N := 8;

8

  

proc (x, s) options operator, arrow; exp(x*s) end proc

  

proc (x) options operator, arrow; exp(2*x)+(exp(x*(x+2))-exp(-x-2))/(x+2) end proc

 (2)
> 

alpha := -1/2;

-1/2

  

-1/2

 (3)
> 

for n from 0 to N+1 do J[n] := unapply(simplify((-1)^n*(1-x)^(-alpha)*(1+x)^(-beta)*(diff((1-x)^(n+alpha)*(1+x)^(n+beta), [`$`(x, n)]))/(2^n*factorial(n))), x) end do;

proc (x) options operator, arrow; 1 end proc

  

proc (x) options operator, arrow; (1/2)*x end proc

  

proc (x) options operator, arrow; (3/4)*x^2-3/8 end proc

  

proc (x) options operator, arrow; (5/4)*x^3-(15/16)*x end proc

  

proc (x) options operator, arrow; (35/16)*x^4-(35/16)*x^2+35/128 end proc

  

proc (x) options operator, arrow; (315/256)*x+(63/16)*x^5-(315/64)*x^3 end proc

  

proc (x) options operator, arrow; (231/32)*x^6-231/1024-(693/64)*x^4+(2079/512)*x^2 end proc

  

proc (x) options operator, arrow; -(3003/2048)*x+(429/32)*x^7-(3003/128)*x^5+(3003/256)*x^3 end proc

  

proc (x) options operator, arrow; (6435/256)*x^8+6435/32768-(6435/128)*x^6+(32175/1024)*x^4-(6435/1024)*x^2 end proc

  

proc (x) options operator, arrow; (109395/65536)*x+(12155/256)*x^9-(109395/1024)*x^7+(328185/4096)*x^5-(182325/8192)*x^3 end proc

 (4)
> 

u := unapply(exp(2*x), x);

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

 (5)
> 

for i from 0 to N do phi[i] := J[i](x) end do

1

  

(1/2)*x

  

(3/4)*x^2-3/8

  

(5/4)*x^3-(15/16)*x

  

(35/16)*x^4-(35/16)*x^2+35/128

  

(315/256)*x+(63/16)*x^5-(315/64)*x^3

  

(231/32)*x^6-231/1024-(693/64)*x^4+(2079/512)*x^2

  

-(3003/2048)*x+(429/32)*x^7-(3003/128)*x^5+(3003/256)*x^3

  

(6435/256)*x^8+6435/32768-(6435/128)*x^6+(32175/1024)*x^4-(6435/1024)*x^2

 (6)
> 

w1 := (1-x)^alpha*(1+x)^beta;

1/((1-x)^(1/2)*(1+x)^(1/2))

 (7)
> 

for j from 0 to N do S[j] := simplify(evalf(int(k(x, s)*subs(x = s, phi[j]), s = -1 .. x))) end do;

(-1.*exp(-1.*x)+1.*exp(x^2))/x

  

.5*(exp(x^2)*x^2+exp(-1.*x)*x+exp(-1.*x)-exp(x^2))/x^2

  

((.75*x^4-1.875*x^2+1.5)*exp(x^2)-.375*(x+2.)^2*exp(-1.*x))/x^3

  

((1.25*x^6-4.6875*x^4+8.4375*x^2-7.5)*exp(x^2)+(.3125*x^3+2.8125*x^2+7.5*x+7.5)*exp(-1.*x))/x^4

  

((2.1875*x^8-10.9375*x^6+30.8984375*x^4-56.875*x^2+52.5)*exp(x^2)+(-.2734375*x^4-4.375*x^3-21.875*x^2-52.5*x-52.5)*exp(-1.*x))/x^5

  

((3.9375*x^10-24.609375*x^8+94.74609375*x^6-267.01171875*x^4+502.03125*x^2-472.5)*exp(x^2)+(.24609375*x^5+6.15234375*x^4+49.21875*x^3+206.71875*x^2+472.5*x+472.5)*exp(-1.*x))/x^6

  

((7.21875*x^12-54.140625*x^10+263.935546875*x^8-1004.5341796875*x^6+2866.74609375*x^4-5457.375*x^2+5197.5)*exp(x^2)+(-.2255859375*x^6-8.12109375*x^5-94.74609375*x^4-606.375*x^3-2338.875*x^2-5197.5*x-5197.5)*exp(-1.*x))/x^7

  

((13.40625*x^14-117.3046875*x^12+692.09765625*x^10-3321.18896484375*x^8+12740.75537109375*x^6-36669.4453125*x^4+70382.8125*x^2-67567.5)*exp(x^2)+(.20947265625*x^7+10.26416015625*x^6+164.2265625*x^5+1478.0390625*x^4+8445.9375*x^3+30968.4375*x^2+67567.5*x+67567.5)*exp(-1.*x))/x^8

  

((25.13671875*x^16-251.3671875*x^14+1740.7177734375*x^12-10086.1083984375*x^10+48652.315521240234375*x^8-187783.857421875*x^6+543707.2265625*x^4-1049709.375*x^2+1013512.5)*exp(x^2)+(-.196380615234375*x^8-12.568359375*x^7-263.935546875*x^6-3167.2265625*x^5-24885.3515625*x^4-132721.875*x^3-470559.375*x^2-1013512.5*x-1013512.5)*exp(-1.*x))/x^9

 (8)
> 

A := Matrix(N+1, N+1):
> 

for i from 0 to N do for j from 0 to N do A[i+1, j+1] := evalf(Int(phi[i]*phi[j]*w1, x = -1 .. 1, epsilon = 0.1e-24)) end do end do;
> 

A

Matrix([[3.14159265358979323846264338328, 0., 0.111111111111111111111111111111e-32, 0., -0.333333333333333333333333333333e-32, 0., -0.173333333333333333333333333333e-31, 0., -0.291851851851851851851851851852e-30], [0., .392699081698724154807830422910, 0., 0.370370370370370370370370370370e-33, 0., -0.370370370370370370370370370370e-33, 0., -0.718518518518518518518518518519e-32, 0.], [0.111111111111111111111111111111e-32, 0., .220893233455532337079404612887, 0., 0.407407407407407407407407407407e-33, 0., 0.666666666666666666666666666667e-32, 0., 0.966666666666666666666666666667e-31], [0., 0.370370370370370370370370370370e-33, 0., .153398078788564122971808758949, 0., 0.740740740740740740740740740741e-33, 0., 0.128888888888888888888888888889e-31, 0.], [-0.333333333333333333333333333333e-32, 0., 0.407407407407407407407407407407e-33, 0., .117445404072494406650291081070, 0., -0.429629629629629629629629629630e-32, 0., -0.459259259259259259259259259259e-31], [0., -0.370370370370370370370370370370e-33, 0., 0.740740740740740740740740740741e-33, 0., 0.951307772987204693867357756671e-1, 0., -0.135555555555555555555555555556e-31, 0.], [-0.173333333333333333333333333333e-31, 0., 0.666666666666666666666666666667e-32, 0., -0.429629629629629629629629629630e-32, 0., 0.799362781468415055263543670536e-1, 0., 0.157777777777777777777777777778e-31], [0., -0.718518518518518518518518518519e-32, 0., 0.128888888888888888888888888889e-31, 0., -0.135555555555555555555555555556e-31, 0., 0.689246479939602777242545307758e-1, 0.], [-0.291851851851851851851851851852e-30, 0., 0.966666666666666666666666666667e-31, 0., -0.459259259259259259259259259259e-31, 0., 0.157777777777777777777777777778e-31, 0., 0.605783039009416503435830836897e-1]])

 (9)
> 

B := Matrix(N+1, N+1):
> 

for j from 0 to N do for i from 0 to N do B[i+1, j+1] := evalf(Int(simplify(phi[i]*S[j]*w1), x = -1 .. 1, epsilon = 0.1e-5), 15) end do end do;
> 

B := Matrix(B)

B := Matrix(9, 9, {(1, 1) = 3.41340669637960, (1, 2) = -.219853801558141, (1, 3) = -.371445167328337, (1, 4) = -0.940736800940411e-2, (1, 5) = -0.845889943042008e-1, (1, 6) = 0.334727115780295e-1, (1, 7) = -0.257221402047336e84, (1, 8) = Float(infinity), (1, 9) = Float(undefined), (2, 1) = .765483256689808, (2, 2) = .141014141031686, (2, 3) = -.165532642864785, (2, 4) = -0.499428359428865e-1, (2, 5) = -0.73434901130578e-2, (2, 6) = -0.111757807839544e-1, (2, 7) = 0.123803381671991e68, (2, 8) = Float(undefined), (2, 9) = Float(-infinity), (3, 1) = 0.515972557667626e-1, (3, 2) = .125811948358948, (3, 3) = 0.408759073542022e-2, (3, 4) = -0.716662760034337e-1, (3, 5) = -0.51685004360437e-2, (3, 6) = 0.716801959003042e67, (3, 7) = Int((43.3125*(2.*x^2-1.)*(0.625e-1*x^12-.46875*x^10+2.28515625*x^8-8.697265625*x^6+24.8203125*x^4-47.25*x^2+45.)*exp(x^2)+43.3125*(2.*x^2-1.)*(-0.1953125e-2*x^6-0.703125e-1*x^5-.8203125*x^4-5.25*x^3-20.25*x^2-45.*x-45.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-1.*x)^(1/2)*x^7), x = -1. .. 1.), (3, 8) = Float(-infinity), (3, 9) = Float(infinity), (4, 1) = 0.899030920810901e-1, (4, 2) = 0.21384118669396e-2, (4, 3) = 0.393313755295959e-1, (4, 4) = -0.17596837269261e-3, (4, 5) = -0.341293873201944e-1, (4, 6) = -0.107499338429209e52, (4, 7) = 0.188236331912532e46, (4, 8) = Float(-infinity), (4, 9) = Int(0.625000000000000e-1*((-15202687.5+502.73437500*x^18-5404.39453125*x^16+38584.8632812500*x^14-227832.934570312*x^12+1124337.93640137*x^10-4485461.88125610*x^8+13690902.3925781*x^6-29149795.8984375*x^4+36015890.625*x^2)*exp(x^2)+5.*(4.*x^2-3.)*(-.196380615234375*x^8-12.568359375*x^7-263.935546875*x^6-3167.2265625*x^5-24885.3515625*x^4-132721.875*x^3-470559.375*x^2-1013512.5*x-1013512.5)*exp(-1.*x))/((1.+x)^(1/2)*(1.-1.*x)^(1/2)*x^8), x = -1. .. 1.), (5, 1) = 0.463651486782722e-3, (5, 2) = 0.157757505144122e-1, (5, 3) = 0.7529674755144e-4, (5, 4) = 0.205695133452456e-1, (5, 5) = 0.323627840089429e50, (5, 6) = -0.194229780735106e-1, (5, 7) = Int((31.58203125*(8.*x^4-8.*x^2+1.)*(0.625e-1*x^12-.46875*x^10+2.28515625*x^8-8.697265625*x^6+24.8203125*x^4-47.25*x^2+45.)*exp(x^2)+31.58203125*(8.*x^4-8.*x^2+1.)*(-0.1953125e-2*x^6-0.703125e-1*x^5-.8203125*x^4-5.25*x^3-20.25*x^2-45.*x-45.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-1.*x)^(1/2)*x^7), x = -1. .. 1.), (5, 8) = Float(infinity), (5, 9) = Float(-infinity), (6, 1) = 0.63086454697723e-2, (6, 2) = 0.148539925067e-4, (6, 3) = 0.678853225186884e-2, (6, 4) = 0.10778334378e-5, (6, 5) = 0.131282639565718e-1, (6, 6) = -0.271179086613e-5, (6, 7) = -0.124971422339580e-1, (6, 8) = -0.810764520616245e86, (6, 9) = 0.973719186742316e103, (7, 1) = 0.225892591375e-5, (7, 2) = 0.119535935984917e-2, (7, 3) = 0.47254024736e-6, (7, 4) = 0.406635846209016e-2, (7, 5) = -0.353102865787386e29, (7, 6) = 0.914224761911803e-2, (7, 7) = Int(0.976562500000000e-3*(231.*(32.*x^6-48.*x^4+18.*x^2-1.)*(7.21875*x^12-54.140625*x^10+263.935546875*x^8-1004.5341796875*x^6+2866.74609375*x^4-5457.375*x^2+5197.5)*exp(x^2)+231.*(32.*x^6-48.*x^4+18.*x^2-1.)*(-.2255859375*x^6-8.12109375*x^5-94.74609375*x^4-606.375*x^3-2338.875*x^2-5197.5*x-5197.5)*exp(-1.*x))/((1.+x)^(1/2)*(1.-1.*x)^(1/2)*x^7), x = -1. .. 1.), (7, 8) = Int(0.976562500000000e-3*(231.*(32.*x^6-48.*x^4+18.*x^2-1.)*(13.40625*x^14-117.3046875*x^12+692.09765625*x^10-3321.18896484375*x^8+12740.7553710938*x^6-36669.4453125*x^4+70382.8125*x^2-67567.5)*exp(x^2)+231.*(32.*x^6-48.*x^4+18.*x^2-1.)*(.20947265625*x^7+10.26416015625*x^6+164.2265625*x^5+1478.0390625*x^4+8445.9375*x^3+30968.4375*x^2+67567.5*x+67567.5)*exp(-1.*x))/((1.+x)^(1/2)*(1.-1.*x)^(1/2)*x^8), x = -1. .. 1.), (7, 9) = Int(0.976562500000000e-3*(231.*(32.*x^6-48.*x^4+18.*x^2-1.)*(25.13671875*x^16-251.3671875*x^14+1740.7177734375*x^12-10086.1083984375*x^10+48652.3155212402*x^8-187783.857421875*x^6+543707.2265625*x^4-1049709.375*x^2+1013512.5)*exp(x^2)+231.*(32.*x^6-48.*x^4+18.*x^2-1.)*(-.196380615234375*x^8-12.568359375*x^7-263.935546875*x^6-3167.2265625*x^5-24885.3515625*x^4-132721.875*x^3-470559.375*x^2-1013512.5*x-1013512.5)*exp(-1.*x))/((1.+x)^(1/2)*(1.-1.*x)^(1/2)*x^9), x = -1. .. 1.), (8, 1) = 0.340365610524644e-3, (8, 2) = 0.5813755404e-7, (8, 3) = 0.59941816605747e-3, (8, 4) = 0.1233441019e-7, (8, 5) = 0.275221040025479e-2, (8, 6) = -0.804784322e-8, (8, 7) = -0.187505962866890e33, (8, 8) = Int(0.488281250000000e-3*(429.*(64.*x^6-112.*x^4+56.*x^2-7.)*(13.40625*x^14-117.3046875*x^12+692.09765625*x^10-3321.18896484375*x^8+12740.7553710938*x^6-36669.4453125*x^4+70382.8125*x^2-67567.5)*exp(x^2)+429.*(64.*x^6-112.*x^4+56.*x^2-7.)*(.20947265625*x^7+10.26416015625*x^6+164.2265625*x^5+1478.0390625*x^4+8445.9375*x^3+30968.4375*x^2+67567.5*x+67567.5)*exp(-1.*x))/((1.+x)^(1/2)*(1.-1.*x)^(1/2)*x^7), x = -1. .. 1.), (8, 9) = Int(0.488281250000000e-3*(429.*(64.*x^6-112.*x^4+56.*x^2-7.)*(25.13671875*x^16-251.3671875*x^14+1740.7177734375*x^12-10086.1083984375*x^10+48652.3155212402*x^8-187783.857421875*x^6+543707.2265625*x^4-1049709.375*x^2+1013512.5)*exp(x^2)+429.*(64.*x^6-112.*x^4+56.*x^2-7.)*(-.196380615234375*x^8-12.568359375*x^7-263.935546875*x^6-3167.2265625*x^5-24885.3515625*x^4-132721.875*x^3-470559.375*x^2-1013512.5*x-1013512.5)*exp(-1.*x))/((1.+x)^(1/2)*(1.-1.*x)^(1/2)*x^8), x = -1. .. 1.), (9, 1) = 0.6793714722e-8, (9, 2) = 0.68406690337078e-4, (9, 3) = 0.1624492831e-8, (9, 4) = 0.386156856246160e-3, (9, 5) = 0.815546544069708e28, (9, 6) = -0.277132564813689e67, (9, 7) = Int(0.305175781250000e-4*(6435.*(128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(7.21875*x^12-54.140625*x^10+263.935546875*x^8-1004.5341796875*x^6+2866.74609375*x^4-5457.375*x^2+5197.5)*exp(x^2)+6435.*(128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(-.2255859375*x^6-8.12109375*x^5-94.74609375*x^4-606.375*x^3-2338.875*x^2-5197.5*x-5197.5)*exp(-1.*x))/((1.+x)^(1/2)*(1.-1.*x)^(1/2)*x^7), x = -1. .. 1.), (9, 8) = Int(0.305175781250000e-4*(6435.*(128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(13.40625*x^14-117.3046875*x^12+692.09765625*x^10-3321.18896484375*x^8+12740.7553710938*x^6-36669.4453125*x^4+70382.8125*x^2-67567.5)*exp(x^2)+6435.*(128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(.20947265625*x^7+10.26416015625*x^6+164.2265625*x^5+1478.0390625*x^4+8445.9375*x^3+30968.4375*x^2+67567.5*x+67567.5)*exp(-1.*x))/((1.+x)^(1/2)*(1.-1.*x)^(1/2)*x^8), x = -1. .. 1.), (9, 9) = Int(0.305175781250000e-4*(6435.*(128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(25.13671875*x^16-251.3671875*x^14+1740.7177734375*x^12-10086.1083984375*x^10+48652.3155212402*x^8-187783.857421875*x^6+543707.2265625*x^4-1049709.375*x^2+1013512.5)*exp(x^2)+6435.*(128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(-.196380615234375*x^8-12.568359375*x^7-263.935546875*x^6-3167.2265625*x^5-24885.3515625*x^4-132721.875*x^3-470559.375*x^2-1013512.5*x-1013512.5)*exp(-1.*x))/((1.+x)^(1/2)*(1.-1.*x)^(1/2)*x^9), x = -1. .. 1.)})

 (10)
> 

G := Vector(N+1):
> 

for i from 0 to N do G[i+1] := evalf(Int(phi[i]*g(x)*w1, x = -1 .. 1, epsilon = 0.1e-24)) end do;

12.1371438004283064513879002531

  

4.46097069166807099930513349705

  

1.64462130209908212771492915391

  

.558865818865511551008391285165

  

.171719662671619385727054996451

  

0.517117975778639694922219536331e-1

  

0.149941760016965250201187504967e-1

  

0.424140250877931274184205530350e-2

  

0.114813711532765772695860143813e-2

 (11)
> 

G[1]

12.1371438004283064513879002531

 (12)
> 

C := simplify(Matrix(A+B))

C := Matrix(9, 9, {(1, 1) = 6.55499934996939323846264338328, (1, 2) = -.219853801558141, (1, 3) = -.371445167328337, (1, 4) = -0.940736800940411e-2, (1, 5) = -0.845889943042008000000000000000e-1, (1, 6) = 0.334727115780295e-1, (1, 7) = -0.257221402047336e84, (1, 8) = Float(infinity), (1, 9) = Float(undefined), (2, 1) = .765483256689808, (2, 2) = .533713222730410154807830422910, (2, 3) = -.165532642864785, (2, 4) = -0.499428359428865e-1, (2, 5) = -0.73434901130578e-2, (2, 6) = -0.111757807839544e-1, (2, 7) = 0.123803381671991e68, (2, 8) = Float(undefined), (2, 9) = Float(-infinity), (3, 1) = 0.515972557667626000000000000000e-1, (3, 2) = .125811948358948, (3, 3) = .224980824190952557079404612887, (3, 4) = -0.716662760034337e-1, (3, 5) = -0.516850043604370000000000000000e-2, (3, 6) = 0.716801959003042e67, (3, 7) = 0.666666666666666666666666666667e-32+43.3125*(Int(((-45.+.1250*x^14-1.00000*x^12+5.03906250*x^10-19.679687500*x^8+58.337890625*x^6-119.3203125*x^4+137.25*x^2)*exp(x^2)+(2.*x^2-1.)*(-0.1953125e-2*x^6-0.703125e-1*x^5-.8203125*x^4-5.25*x^3-20.25*x^2-45.*x-45.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-x)^(1/2)*x^7), x = -1. .. 1.)), (3, 8) = Float(-infinity), (3, 9) = Float(infinity), (4, 1) = 0.899030920810901e-1, (4, 2) = 0.213841186693960000000000000000e-2, (4, 3) = 0.393313755295959e-1, (4, 4) = .153222110415871512971808758949, (4, 5) = -0.341293873201944e-1, (4, 6) = -0.107499338429209e52, (4, 7) = 0.188236331912532e46, (4, 8) = Float(-infinity), (4, 9) = 0.3125e-1*(Int(((-30405375.+1005.46875*x^18-10808.7890625*x^16+77169.7265625*x^14-455665.869140624*x^12+2248675.87280274*x^10-8970923.7625122*x^8+27381804.7851562*x^6-58299591.796875*x^4+72031781.25*x^2)*exp(x^2)+(-7.855224609375*x^10-502.734375*x^9-10551.53045654296875*x^8-126312.01171875*x^7-987495.99609375*x^6-5213858.203125*x^5-18075814.453125*x^4-36558843.75*x^3-26423718.75*x^2+30405375.*x+30405375.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-x)^(1/2)*x^8), x = -1. .. 1.)), (5, 1) = 0.463651486782721999999999999997e-3, (5, 2) = 0.157757505144122e-1, (5, 3) = 0.752967475514400000000000000004e-4, (5, 4) = 0.205695133452456e-1, (5, 5) = 0.323627840089429e50, (5, 6) = -0.194229780735106e-1, (5, 7) = -0.429629629629629629629629629630e-32+31.58203125*(Int(((8.*x^4-8.*x^2+1.)*(0.625e-1*x^12-.46875*x^10+2.28515625*x^8-8.697265625*x^6+24.8203125*x^4-47.25*x^2+45.)*exp(x^2)+(8.*x^4-8.*x^2+1.)*(-0.1953125e-2*x^6-0.703125e-1*x^5-.8203125*x^4-5.25*x^3-20.25*x^2-45.*x-45.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-x)^(1/2)*x^7), x = -1. .. 1.)), (5, 8) = Float(infinity), (5, 9) = Float(-infinity), (6, 1) = 0.63086454697723e-2, (6, 2) = 0.148539925066999999999999999996e-4, (6, 3) = 0.678853225186884e-2, (6, 4) = 0.107783343780000000000000000074e-5, (6, 5) = 0.131282639565718e-1, (6, 6) = 0.951280655078543393867357756671e-1, (6, 7) = -0.124971422339580e-1, (6, 8) = -0.810764520616245e86, (6, 9) = 0.973719186742316e103, (7, 1) = 0.225892591374999999999999998267e-5, (7, 2) = 0.119535935984917e-2, (7, 3) = 0.472540247360000000000000006667e-6, (7, 4) = 0.406635846209016e-2, (7, 5) = -0.353102865787386e29, (7, 6) = 0.914224761911803e-2, (7, 7) = 0.799362781468415055263543670536e-1+26.05517578125*(Int(((32.*x^6-48.*x^4+18.*x^2-1.)*(0.625e-1*x^12-.46875*x^10+2.28515625*x^8-8.697265625*x^6+24.8203125*x^4-47.25*x^2+45.)*exp(x^2)+(32.*x^6-48.*x^4+18.*x^2-1.)*(-0.1953125e-2*x^6-0.703125e-1*x^5-.8203125*x^4-5.25*x^3-20.25*x^2-45.*x-45.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-x)^(1/2)*x^7), x = -1. .. 1.)), (7, 8) = .11279296875*(Int(((32.*x^6-48.*x^4+18.*x^2-1.)*(26.8125*x^14-234.609375*x^12+1384.1953125*x^10-6642.3779296875*x^8+25481.5107421876*x^6-73338.890625*x^4+140765.625*x^2-135135.)*exp(x^2)+(32.*x^6-48.*x^4+18.*x^2-1.)*(.4189453125*x^7+20.5283203125*x^6+328.453125*x^5+2956.078125*x^4+16891.875*x^3+61936.875*x^2+135135.*x+135135.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-x)^(1/2)*x^8), x = -1. .. 1.)), (7, 9) = 0.157777777777777777777777777778e-31+1.24072265625*(Int(((32.*x^6-48.*x^4+18.*x^2-1.)*(4.5703125*x^16-45.703125*x^14+316.494140625*x^12-1833.837890625*x^10+8845.8755493164*x^8-34142.51953125*x^6+98855.859375*x^4-190856.25*x^2+184275.)*exp(x^2)+(32.*x^6-48.*x^4+18.*x^2-1.)*(-0.3570556640625e-1*x^8-2.28515625*x^7-47.98828125*x^6-575.859375*x^5-4524.609375*x^4-24131.25*x^3-85556.25*x^2-184275.*x-184275.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-x)^(1/2)*x^9), x = -1. .. 1.)), (8, 1) = 0.340365610524644e-3, (8, 2) = 0.581375540399999999999999928148e-7, (8, 3) = 0.59941816605747e-3, (8, 4) = 0.123344101900000000000000128889e-7, (8, 5) = 0.275221040025479e-2, (8, 6) = -0.804784322000000000000001355556e-8, (8, 7) = -0.187505962866890e33, (8, 8) = 0.689246479939602777242545307758e-1+.104736328125*(Int(((64.*x^6-112.*x^4+56.*x^2-7.)*(26.8125*x^14-234.609375*x^12+1384.1953125*x^10-6642.3779296875*x^8+25481.5107421876*x^6-73338.890625*x^4+140765.625*x^2-135135.)*exp(x^2)+(64.*x^6-112.*x^4+56.*x^2-7.)*(.4189453125*x^7+20.5283203125*x^6+328.453125*x^5+2956.078125*x^4+16891.875*x^3+61936.875*x^2+135135.*x+135135.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-x)^(1/2)*x^7), x = -1. .. 1.)), (8, 9) = 1.152099609375*(Int(((64.*x^6-112.*x^4+56.*x^2-7.)*(4.5703125*x^16-45.703125*x^14+316.494140625*x^12-1833.837890625*x^10+8845.8755493164*x^8-34142.51953125*x^6+98855.859375*x^4-190856.25*x^2+184275.)*exp(x^2)+(64.*x^6-112.*x^4+56.*x^2-7.)*(-0.3570556640625e-1*x^8-2.28515625*x^7-47.98828125*x^6-575.859375*x^5-4524.609375*x^4-24131.25*x^3-85556.25*x^2-184275.*x-184275.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-x)^(1/2)*x^8), x = -1. .. 1.)), (9, 1) = 0.679371472199999999999970814815e-8, (9, 2) = 0.68406690337078e-4, (9, 3) = 0.162449283100000000000009666667e-8, (9, 4) = 0.386156856246160e-3, (9, 5) = 0.815546544069708e28, (9, 6) = -0.277132564813689e67, (9, 7) = 0.157777777777777777777777777778e-31+22.6819610595703125*(Int(((128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(0.625e-1*x^12-.46875*x^10+2.28515625*x^8-8.697265625*x^6+24.8203125*x^4-47.25*x^2+45.)*exp(x^2)+(128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(-0.1953125e-2*x^6-0.703125e-1*x^5-.8203125*x^4-5.25*x^3-20.25*x^2-45.*x-45.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-x)^(1/2)*x^7), x = -1. .. 1.)), (9, 8) = 0.196380615234375e-1*(Int(((128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(134.0625*x^14-1173.046875*x^12+6920.9765625*x^10-33211.8896484375*x^8+127407.553710938*x^6-366694.453125*x^4+703828.125*x^2-675675.)*exp(x^2)+(128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(2.0947265625*x^7+102.6416015625*x^6+1642.265625*x^5+14780.390625*x^4+84459.375*x^3+309684.375*x^2+675675.*x+675675.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-x)^(1/2)*x^8), x = -1. .. 1.)), (9, 9) = 0.605783039009416503435830836897e-1+.2160186767578125*(Int(((128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(22.8515625*x^16-228.515625*x^14+1582.470703125*x^12-9169.189453125*x^10+44229.377746582*x^8-170712.59765625*x^6+494279.296875*x^4-954281.25*x^2+921375.)*exp(x^2)+(128.*x^8-256.*x^6+160.*x^4-32.*x^2+1.)*(-.17852783203125*x^8-11.42578125*x^7-239.94140625*x^6-2879.296875*x^5-22623.046875*x^4-120656.25*x^3-427781.25*x^2-921375.*x-921375.)*exp(-1.*x))/((1.+x)^(1/2)*(1.-x)^(1/2)*x^9), x = -1. .. 1.))})

 (13)
> 

C1 := MatrixInverse(C)

Warning,  computation interrupted

  
> 

``
> 

t := C1.G
> 

s[u] := add(subs(theta = sols[l+1], ((x+1)*(1/2))*k(x, ss(x, theta)))*u(ss(x, sols[l+1])), l = 0 .. N)
> 

U := unapply(add(t[j+1].phi[j], j = 0 .. N), x)
> 

``
> 

with(numapprox)
> 

E := infnorm(abs(u(x)-U(x)), x = -1 .. 1)
> 

``
> 

E[1] := (int((u(x)-U(x))^2, x = -1 .. .1))^(1/2)
> 

``
> 

plot([U(x), u(x)], x = -1 .. 1)
> 

 

``

> 

NULL

 

Download chebichef_cont.mw

Solve Simple Equation...

Asked by: Parham2016 70
polynomial rootof
August 14 2016
0  2

 Hi all,

 Is there anyone who could help me with this error? I am sure there is at least one solution for the equation.

 Thanks

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/EQ.mw .

Download EQ.mw

Set Theory, how to create 'set functions' in Maple...

Asked by: cipri 5
logic set
August 14 2016
1  2

Typically sets are created like:

A:={a,b,c};

B:={c,q,w,e};

and then you can carryout A union B or B\A

 

what if  you wanted to create the set as

A:={values in some three dimensional space};

B:={volume, based on values taken from A};

Can these relationships be set up in Maple? If so, how? If there are commands that specifically handle these types of sets, what does maple call them?  I've seen the term 'set function' but what might Maple call them?

Note: I am not even sure i 'tagged' this correctly because it I am not sure the proper terms for these functions/sets.

Thanks in advance for any help.

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