MaplePrimes Questions

Hello.

 

I have been trying to create a code to solve a structure by using FEM, but I keep getting an error that stops me from moving on.

 

Everytime I run my code, Maple gives me the error in the Title of my question:
"Error, number of indices exceeds rank"

 

Unfortunately I can't find any help in Maplesoft support for such error, and I need immediate help for that.

Can someone help me with that? Should I post my entire code?

Thanks!

Hi everyone, 

I often get the error 'cannot save points as a float matrix' while I'm trying to plot with the spacecurve command.

loodl2 is a 4 component vector, loodl2c is the 3 component variant.

loodl2:=T1.<loodl,1>: loodl2c:=<loodl2[1], loodl2[2], loodl2[3]>
loodlpl:=spacecurve(loodl2c, k=-10..10, color=red):

also with this syntax:
loodl2c:=loodl2[1..3]

and this syntax:

l2c1:= 2*k: l2c2:=0, l2c3:=8-k:
spacecurve([l2c1, l2c2, l2c3], k=-10..10, color=red):
Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

It will only plot if I do this:
loodl2c:=<2*k, 0, 8-k>
Can someone help me?
 

I am trying to use the element properties Maple has in its ScientificConstants package. I am running into problems with the density of gaseous elements:

with(ScientificConstants);

Units:-UsingSystem(); # returns SI as expected

GetValue(Element('Si',density)); # returns 2329.0000 [kg/m^3] which is 2.329 g/cm^3, which is correct

GetValue(Element('H',density(gas))); # returns 88 [kg/m^3], which is incorrect.

PDG gives the density of hydrogen as 8.376E-5 g/cm^3, which is 0.08376 kg/m^3.  

Even more crazy for Krypton:

GetValue(Element('Kr',density(gas))); # returns 3677.000 [kg/m^3]. Heavy little buggers, these Kypton atoms! Should be 3.486 in the same units.

What gives? Am I missing something here?

Mac Dude

 

 

In matlab there is a sqrtm() command to calculate the square root of square matrices, I want to know if there is a similar command in Maple to do same thing?

What is the meaning of the "0" in the series expansion

series(x/(-x2-x+1), x = 0); ( this is the Maple command)
                   
              x + x2  + 2 x3  + 3 x4 + 5 x5  + O(x6)  This is the results

This is use in Maple I've seen quite a bit for series. I assume the the series continues on. But I am not sure

Also is there any listing of what some of the symbols that maple uses???
 

Is there a way to specify different colors for different output variables? For example, if x,y, and z appear in the entire document as variables, I want x to be red, y to be blue, and z to be green whenever an output is displayed.

Thanks

hi..how i can rewrite section of this code as another form i,e ''for section''

I have a lot of line as this and runnig cise is time consuming.

is there another way to write this section in order to the runtime of the program is reduced??

thanks

for.mw
 

restart;

with(LinearAlgebra):

with(VectorCalculus):

#Digits:=5:
k:=6:

l:=0:

h:=1:

m:=4:

n:=4:

l1:=2*h:

l2:=2*h:

N:=0.5:

nu:=.3:

E_m:=70e9:

E_c:=380e9:

rho_m:=2702:

rho_c:=3800:

lambda_m:=nu*E_m/((1+nu)*(1-2*nu)):

lambda_c:=nu*E_c/((1+nu)*(1-2*nu)):

mu_m:=E_m/(2*(1+nu)):

mu_c:=E_c/(2*(1+nu)):

with(orthopoly):

for i from 0 to 5 do:
L(i):=sqrt((2*i+1)/2)*P(i,z):
end do:

Z:=rho_m+(rho_c-rho_m)*((1/2)+(z/h))^N;

2702+1098*(1/2+z)^.5

(1)

U:=lambda_m+(lambda_c-lambda_m)*((1/2)+(z/h))^N;

0.4038461538e11+0.1788461538e12*(1/2+z)^.5

(2)

S:=mu_m+(mu_c-mu_m)*((1/2)+(z/h))^N;

0.2692307692e11+0.1192307692e12*(1/2+z)^.5

(3)

d:=Matrix([[0,0,0,0,0,0,0,0],[sqrt(3),0,0,0,0,0,0,0],[0,sqrt(15),0,0,0,0,0,0],[sqrt(7),0,sqrt(35),0,0,0,0,0],[0,sqrt(27),0,sqrt(63),0,0,0,0],[sqrt(11),0,sqrt(55),0,sqrt(99),0,0,0],[0,sqrt(39),0,sqrt(91),0,sqrt(143),0,0],[sqrt(15),0,sqrt(75),0,sqrt(135),0,sqrt(195),0]]);

d := Matrix(8, 8, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (2, 1) = 3^(1/2), (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (3, 1) = 0, (3, 2) = 15^(1/2), (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (4, 1) = 7^(1/2), (4, 2) = 0, (4, 3) = 35^(1/2), (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (5, 1) = 0, (5, 2) = 3*3^(1/2), (5, 3) = 0, (5, 4) = 3*7^(1/2), (5, 5) = 0, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (6, 1) = 11^(1/2), (6, 2) = 0, (6, 3) = 55^(1/2), (6, 4) = 0, (6, 5) = 3*11^(1/2), (6, 6) = 0, (6, 7) = 0, (6, 8) = 0, (7, 1) = 0, (7, 2) = 39^(1/2), (7, 3) = 0, (7, 4) = 91^(1/2), (7, 5) = 0, (7, 6) = 143^(1/2), (7, 7) = 0, (7, 8) = 0, (8, 1) = 15^(1/2), (8, 2) = 0, (8, 3) = 5*3^(1/2), (8, 4) = 0, (8, 5) = 3*15^(1/2), (8, 6) = 0, (8, 7) = 195^(1/2), (8, 8) = 0})

(4)

``

``

e2 := 0;

0

 

-0.3192307692e12*W(1)+0.4396880662e12*W(3)-0.1474586301e12*W(5)-0.9235575669e11*W(2)+0.1979090105e12*W(4)

(5)

``


 

Download for.mw

 

hi...

how I can dsolve this differential equations. parameter p is unkown.

I want to gain w(x) and u(x) and psi(x) and p.

thanks

sade.mw
 

restart; eq1 := (diff(psi(x), x))^2+(diff(u(x), x)+(8*(1/2))*(diff(w(x), x))^2)((diff(psi(x), x))^2)+3*(diff(w(x), x, x))+5*(diff(w(x), x, x))*(diff(psi(x), x))-7*(diff(u(x), x, x, x)+(8*(1/2))*(diff(w(x), x, x))^2+(3/2)*(diff(w(x), x, x, x))*(diff(w(x), x)))+3 = p

(diff(psi(x), x))^2+(diff(u(x), x))((diff(psi(x), x))^2)+4*(diff(w(x), x))((diff(psi(x), x))^2)^2+3*(diff(diff(w(x), x), x))+5*(diff(diff(w(x), x), x))*(diff(psi(x), x))-7*(diff(diff(diff(u(x), x), x), x))-28*(diff(diff(w(x), x), x))^2-(21/2)*(diff(diff(diff(w(x), x), x), x))*(diff(w(x), x))+3 = p

(1)

eq2 := (51-31)(diff(psi(x), x, x))+(52-2)(diff(w(x), x, x, x))+8*(diff(psi(x), x, x, x, x))-7*(diff(w(x), x)-psi(x)) = 0

70+8*(diff(diff(diff(diff(psi(x), x), x), x), x))-7*(diff(w(x), x))+7*psi(x) = 0

(2)

eq3 := 4*(diff(w(x), x, x)-(diff(psi(x), x)))+(23+11)(diff(psi(x), x, x, x))+(14+12)*(diff(w(x), x, x, x, x)) = 0

4*(diff(diff(w(x), x), x))-4*(diff(psi(x), x))+34+26*(diff(diff(diff(diff(w(x), x), x), x), x)) = 0

(3)

dsys3 := {eq1, eq2, eq3, psi(0) = 0, psi(1) = 0, u(0) = 0, u(1) = 0, w(0) = 0, w(1) = 0, ((D@@1)(psi))(0) = 0, ((D@@1)(psi))(1) = 0, ((D@@1)(w))(0) = 0, ((D@@1)(w))(1) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 1200, numeric, abserr = .1, output = array([.5]))

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 12, got 10

 

dsolve({eq2, eq3}, {psi(x), w(x)}):

with(PDEtools, casesplit, declare);

[casesplit, declare]

(4)

 


 

Download sade.mw

 

hi...

how i can dsolve this differential equations and obtain w(x) and U(x) and phi(x) analytical or numerically?

thanks

zah.mw
 

``

restart; L := 100; h := 1; eq1 := 1130*(diff(U(x), x, x))+1130*(diff(W(x), x))*(diff(W(x), x, x))+1130*(diff(U(x), x, x, x, x))

1130*(diff(diff(U(x), x), x))+1130*(diff(W(x), x))*(diff(diff(W(x), x), x))+1130*(diff(diff(diff(diff(U(x), x), x), x), x))

(1)

eq2 := 1130*(diff(W(x), x))*(diff(U(x), x, x)+(diff(W(x), x))*(diff(W(x), x, x)))+(diff(W(x), x, x))*(1130*(diff(U(x), x))+565*(diff(W(x), x))^2-2.2*(int(diff(varphi(z), z), z = -5/2 .. 5/2)))+(14125/6)*(diff(W(x), x, x, x, x, x, x))+(10405/6)*(diff(W(x), x, x, x, x))+10

1130*(diff(W(x), x))*(diff(diff(U(x), x), x)+(diff(W(x), x))*(diff(diff(W(x), x), x)))+(diff(diff(W(x), x), x))*(1130*(diff(U(x), x))+565*(diff(W(x), x))^2-2.2*(int(diff(varphi(z), z), z = -5/2 .. 5/2)))+(14125/6)*(diff(diff(diff(diff(diff(diff(W(x), x), x), x), x), x), x))+(10405/6)*(diff(diff(diff(diff(W(x), x), x), x), x))+10

(2)

eq3 := diff(varphi(z), z, z)-.35*(diff(W(x), x, x))

diff(diff(varphi(z), z), z)-.35*(diff(diff(W(x), x), x))

(3)

dsys3 := {eq1, eq2, eq3, U(0) = 0, U(L) = 0, W(0) = 0, W(L) = 0, `&varphi;`(-(1/2)*h) = 0, `&varphi;`(-(1/2)*h) = 2, ((D@@1)(W))(0) = 0, ((D@@1)(W))(L) = 0, ((D@@2)(W))(0) = 0, ((D@@2)(W))(L) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 1200, numeric, abserr = .1, output = array([.5]))

Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {x, z}

 

``


 

Download zah.mw

 

> {w = -4*mu, a[-1] = -12*mu/(a+b), a[0] = a[0], a[1] = 0, b[-1] = 0, b[0] = 0, b[1] = 0};
  /                     12 mu                                              
 { w = -4 mu, a[-1] = - -----, a[0] = a[0], a[1] = 0, b[-1] = 0, b[0] = 0,
  \                     a + b                                              

           \
   b[1] = 0 }
           /
> restart;
>
> w := -4*mu;
                                    -4 mu
> a[-1] := -12*mu/(a+b);
                                     12 mu
                                   - -----
                                     a + b
> a[0] := a[0];
                                    a[0]
> a[1] := 0;
                                      0
> b[-1] := 0;
                                      0
> b[0] := 0;
                                      0
> b[1] := 0;
                                      0
> xi := x+w*t;
                                 x - 4 mu t
> P := sqrt(mu)*tan(A-sqrt(mu)*xi);
                      (1/2)    /      (1/2)             \
                    mu      tan\A - mu      (x - 4 mu t)/
> u := a[0]+a[1]*P/(1+lambda*P)+a[-1]*(1+lambda*P)/P+b[0]*sqrt(sigma*(1+P^2/mu))/P+b[1]*sqrt(sigma*(1+P^2/mu))+b[-1]*sqrt(sigma*(1+P^2/mu))/P^2;
                (1/2) /             (1/2)    /      (1/2)             \\
           12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//
    a[0] - -------------------------------------------------------------
                                  /      (1/2)             \            
                       (a + b) tan\A - mu      (x - 4 mu t)/            
> Diff(u, x, t)+a*(Diff(u, x))*(Diff(u, x, y))+b*(Diff(u, `$`(x, 2)))*(Diff(u, y))+Diff(u, `$`(x, 3), y);
/   2   /            (1/2) /             (1/2)    /      (1/2)             \\\
|  d    |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|
|------ |a[0] - -------------------------------------------------------------|
| dt dx |                              /      (1/2)             \            |
\       \                   (a + b) tan\A - mu      (x - 4 mu t)/            /

  \     /    /    
  |     | d  |    
  | + a |--- |a[0]
  |     | dx |    
  /     \    \    

          (1/2) /             (1/2)    /      (1/2)             \\\\ /   2   /
     12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|| |  d    |
   - -------------------------------------------------------------|| |------ |
                            /      (1/2)             \            || | dy dx |
                 (a + b) tan\A - mu      (x - 4 mu t)/            // \       \

              (1/2) /             (1/2)    /      (1/2)             \\\\     /
         12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//||     |
  a[0] - -------------------------------------------------------------|| + b |
                                /      (1/2)             \            ||     |
                     (a + b) tan\A - mu      (x - 4 mu t)/            //     \

   2 /            (1/2) /             (1/2)    /      (1/2)             \\\\ /
  d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//|| |
  -- |a[0] - -------------------------------------------------------------|| |
     |                              /      (1/2)             \            || |
     \                   (a + b) tan\A - mu      (x - 4 mu t)/            // \

      /            (1/2) /             (1/2)    /      (1/2)             \\\\
   d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//||
  --- |a[0] - -------------------------------------------------------------||
   dy |                              /      (1/2)             \            ||
      \                   (a + b) tan\A - mu      (x - 4 mu t)/            //

     / 4 /            (1/2) /             (1/2)    /      (1/2)             \\
     |d  |       12 mu      \1 + lambda mu      tan\A - mu      (x - 4 mu t)//
   + |-- |a[0] - -------------------------------------------------------------
     |   |                              /      (1/2)             \            
     \   \                   (a + b) tan\A - mu      (x - 4 mu t)/            

  \\
  ||
  ||
  ||
  //
> value(%);
                       /                                 2\
              3        |       /      (1/2)             \ |
         96 mu  lambda \1 + tan\A - mu      (x - 4 mu t)/ /
         --------------------------------------------------
                               a + b                       

                                                                2   
                            /                                 2\    
                   3        |       /      (1/2)             \ |    
              96 mu  lambda \1 + tan\A - mu      (x - 4 mu t)/ /    
            - --------------------------------------------------- +
                                                         2          
                               /      (1/2)             \           
                    (a + b) tan\A - mu      (x - 4 mu t)/           

                                                  /             
                                                  |             
                             1                    |     (5/2) /
           -------------------------------------- \96 mu      \1
                                                3               
                      /      (1/2)             \                
           (a + b) tan\A - mu      (x - 4 mu t)/                

                       (1/2)    /      (1/2)             \\
            + lambda mu      tan\A - mu      (x - 4 mu t)//

                                               2\   
           /                                 2\ |   
           |       /      (1/2)             \ | |   
           \1 + tan\A - mu      (x - 4 mu t)/ / / -

                                                 /             
                             1                   |     (5/2) /
           ------------------------------------- \96 mu      \1
                      /      (1/2)             \               
           (a + b) tan\A - mu      (x - 4 mu t)/               

                                                            /
                       (1/2)    /      (1/2)             \\ |
            + lambda mu      tan\A - mu      (x - 4 mu t)// \1

                                           2\\
                 /      (1/2)             \ ||
            + tan\A - mu      (x - 4 mu t)/ //
> simplify(%);
Error, (in simplify/tools/_zn) too many levels of recursion
>

 

hi every one, i want to plot an indefinite integral  , it is some what complex and maple can not compute the answer, ( but numeric integration can be computed) , but we want to plot the output, what should we do ? tnx for help in advance

corrected.mw

how can we compute wighted norm of a matrix or a vector in maple? 


``

How can I convert the result (2) to equal to the trigonometric identity (kw/s^2)*tanh(a*s/2)?

``

g := kw*piecewise(t < a, t, t < 2*a, 2*a-t)

kw*piecewise(t < a, t, t < 2*a, 2*a-t)

(1)

simplify((int(exp(-s*t)*g, t = 0 .. a)+int(exp(-s*t)*g, t = a .. 2*a))/(1-exp(-2*a*s)))

-(exp(-a*s)-1)*kw/((exp(-a*s)+1)*s^2)

(2)

``


Download trigonometric_id.mw

 

this equation is complicated

how to dsolve for this equation for function f ?

f(t,x,diff(x,t)) - f(t,x,p) - (diff(x,t)-p)*diff(f(t,x,p), p) = tan(t)
 

how to find the contour of time series data? and how to find curvature function of this contour?

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