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Hello Anybody can help me to write codes for PDE to solve by Galerkin finite element method or any other methods can be able to gain results? parameter omega is unknown and should be determined.

I attached a pdf file for more .

Thanks so much


"restart:  rho:=7850:  E:=0.193e12:  n:=1:  AD:=10:  upsilon:=0.291:   mu:=E/(2*(1+upsilon)):  l:=0:  lambda:=E*upsilon/((1+upsilon)*(1-2*upsilon)):  R:=2.5:  ii:=2:  J:=2:       m:=1:       `u__theta`(r,theta,phi):= ( V(r,theta))*cos(m*phi):  `u__r`(r,theta,phi):= ( U(r,theta))*cos(m*phi): `u__phi`(r,theta,phi):= ( W(r,theta))*sin(m*phi):  :        eq1:=(r (R+r cos(theta))^2 (mu+lambda) (((∂)^2)/(∂r∂theta) `u__theta`(r,theta,phi))+2 r^2 (mu+lambda/2) (R+r cos(theta))^2 (((∂)^2)/(∂r^2) `u__r`(r,theta,phi))+r^2 (mu+lambda) (R+r cos(theta)) (((∂)^2)/(∂phi∂r) `u__phi`(r,theta,phi))+mu (R+r cos(theta))^2 (((∂)^2)/(∂theta^2) `u__r`(r,theta,phi))+(((∂)^2)/(∂phi^2) `u__r`(r,theta,phi)) mu r^2-3 (R+r cos(theta))^2 (mu+lambda/3) ((∂)/(∂theta) `u__theta`(r,theta,phi))+2 r (mu+lambda/2) (R+2 r cos(theta)) (R+r cos(theta)) ((∂)/(∂r) `u__r`(r,theta,phi))-r^2 sin(theta) (mu+lambda) (R+r cos(theta)) ((∂)/(∂r) `u__theta`(r,theta,phi))-3 r^2 cos(theta) (mu+lambda/3) ((∂)/(∂phi) `u__phi`(r,theta,phi))-r mu sin(theta) (R+r cos(theta)) ((∂)/(∂theta) `u__r`(r,theta,phi))-2 (mu+lambda/2) (2 (cos(theta))^2 r^2+2 cos(theta) R r+R^2) `u__r`(r,theta,phi)+r `u__theta`(r,theta,phi) sin(theta) (3 r (mu+lambda/3) cos(theta)+R mu))/(r^2 (R+r cos(theta))^2):  eq2:=(2 (mu+lambda/2) (R+r cos(theta))^2 (((∂)^2)/(∂theta^2) `u__theta`(r,theta,phi))+r (R+r cos(theta))^2 (mu+lambda) (((∂)^2)/(∂r∂theta) `u__r`(r,theta,phi))+r (mu+lambda) (R+r cos(theta)) (((∂)^2)/(∂phi∂theta) `u__phi`(r,theta,phi))+r^2 mu (R+r cos(theta))^2 (((∂)^2)/(∂r^2) `u__theta`(r,theta,phi))+(((∂)^2)/(∂phi^2) `u__theta`(r,theta,phi)) mu r^2+3 (R+r cos(theta)) ((4 r (mu+lambda/2) cos(theta))/3+R (mu+lambda/3)) ((∂)/(∂theta) `u__r`(r,theta,phi))-2 r (mu+lambda/2) sin(theta) (R+r cos(theta)) ((∂)/(∂theta) `u__theta`(r,theta,phi))+r mu (R+2 r cos(theta)) (R+r cos(theta)) ((∂)/(∂r) `u__theta`(r,theta,phi))+3 r^2 sin(theta) (mu+lambda/3) ((∂)/(∂phi) `u__phi`(r,theta,phi))+(-3 r R (mu+lambda/3) cos(theta)+(-lambda-2 mu) r^2-R^2 mu) `u__theta`(r,theta,phi)-2 r (mu+lambda/2) sin(theta) R `u__r`(r,theta,phi))/(r^2 (R+r cos(theta))^2):  eq3:=(r (mu+lambda) (R+r cos(theta)) (((∂)^2)/(∂phi∂theta) `u__theta`(r,theta,phi))+r^2 (mu+lambda) (R+r cos(theta)) (((∂)^2)/(∂phi∂r) `u__r`(r,theta,phi))+mu (R+r cos(theta))^2 (((∂)^2)/(∂theta^2) `u__phi`(r,theta,phi))+r (r mu (R+r cos(theta))^2 (((∂)^2)/(∂r^2) `u__phi`(r,theta,phi))+2 r (mu+lambda/2) (((∂)^2)/(∂phi^2) `u__phi`(r,theta,phi))+(4 r (mu+lambda/2) cos(theta)+R (mu+lambda)) ((∂)/(∂phi) `u__r`(r,theta,phi))+mu (R+2 r cos(theta)) (R+r cos(theta)) ((∂)/(∂r) `u__phi`(r,theta,phi))-mu sin(theta) (R+r cos(theta)) ((∂)/(∂theta) `u__phi`(r,theta,phi))-r (3 sin(theta) (mu+lambda/3) ((∂)/(∂phi) `u__theta`(r,theta,phi))+`u__phi`(r,theta,phi) mu)))/(r^2 (R+r cos(theta))^2):  "

EQ1 := collect(eq1, cos(m*phi))/cos(m*phi)+rho*omega^2; EQ2 := collect(eq2, cos(m*phi))/cos(m*phi)+rho*omega^2; EQ3 := collect(eq3, sin(m*phi))/sin(m*phi)+rho*omega^2

(0.1788235818e12*r*(2.5+r*cos(theta))^2*(diff(diff(V(r, theta), r), theta))+0.2535718390e12*r^2*(2.5+r*cos(theta))^2*(diff(diff(U(r, theta), r), r))+0.1788235818e12*r^2*(2.5+r*cos(theta))*(diff(W(r, theta), r))+0.7474825716e11*(2.5+r*cos(theta))^2*(diff(diff(U(r, theta), theta), theta))-0.7474825716e11*U(r, theta)*r^2-0.3283200960e12*(2.5+r*cos(theta))^2*(diff(V(r, theta), theta))+0.2535718390e12*r*(2.5+2.*r*cos(theta))*(2.5+r*cos(theta))*(diff(U(r, theta), r))-0.1788235818e12*r^2*sin(theta)*(2.5+r*cos(theta))*(diff(V(r, theta), r))-0.3283200960e12*r^2*cos(theta)*W(r, theta)-0.7474825716e11*r*sin(theta)*(2.5+r*cos(theta))*(diff(U(r, theta), theta))-0.2535718390e12*(2.*cos(theta)^2*r^2+5.0*r*cos(theta)+6.25)*U(r, theta)+r*V(r, theta)*sin(theta)*(0.3283200960e12*r*cos(theta)+0.1868706429e12))/(r^2*(2.5+r*cos(theta))^2)+7850*omega^2


(0.2535718390e12*(2.5+r*cos(theta))^2*(diff(diff(V(r, theta), theta), theta))+0.1788235818e12*r*(2.5+r*cos(theta))^2*(diff(diff(U(r, theta), r), theta))+0.1788235818e12*r*(2.5+r*cos(theta))*(diff(W(r, theta), theta))+0.7474825716e11*r^2*(2.5+r*cos(theta))^2*(diff(diff(V(r, theta), r), r))-0.7474825716e11*V(r, theta)*r^2+3.*(2.5+r*cos(theta))*(0.1690478927e12*r*cos(theta)+0.2736000800e12)*(diff(U(r, theta), theta))-0.2535718390e12*r*sin(theta)*(2.5+r*cos(theta))*(diff(V(r, theta), theta))+0.7474825716e11*r*(2.5+2.*r*cos(theta))*(2.5+r*cos(theta))*(diff(V(r, theta), r))+0.3283200960e12*r^2*sin(theta)*W(r, theta)+(-0.8208002400e12*r*cos(theta)-0.2535718389e12*r^2-0.4671766072e12)*V(r, theta)-0.6339295976e12*r*sin(theta)*U(r, theta))/(r^2*(2.5+r*cos(theta))^2)+7850*omega^2


(-0.1788235818e12*r*(2.5+r*cos(theta))*(diff(V(r, theta), theta))-0.1788235818e12*r^2*(2.5+r*cos(theta))*(diff(U(r, theta), r))+0.7474825716e11*(2.5+r*cos(theta))^2*(diff(diff(W(r, theta), theta), theta))+r*(0.7474825716e11*r*(2.5+r*cos(theta))^2*(diff(diff(W(r, theta), r), r))-0.2535718390e12*r*W(r, theta)-1.*(0.5071436780e12*r*cos(theta)+0.4470589545e12)*U(r, theta)+0.7474825716e11*(2.5+2.*r*cos(theta))*(2.5+r*cos(theta))*(diff(W(r, theta), r))-0.7474825716e11*sin(theta)*(2.5+r*cos(theta))*(diff(W(r, theta), theta))-1.*r*(-0.3283200960e12*sin(theta)*V(r, theta)+0.7474825716e11*W(r, theta))))/(r^2*(2.5+r*cos(theta))^2)+7850*omega^2


#BCs can be from following
U(0, theta) = 0, (D[1](U))(0, theta) = 0, U(1, theta) = 0, (D[1](U))(1, theta) = 0

U(0, theta) = 0, (D[1](U))(0, theta) = 0, U(1, theta) = 0, (D[1](U))(1, theta) = 0


V(0, theta) = 0, (D[1](V))(0, theta) = 0, V(1, theta) = 0, (D[1](V))(1, theta) = 0
W(0, theta) = 0, (D[1](W))(0, theta) = 0, W(1, theta) = 0, (D[1](W))(1, theta) = 0

V(0, theta) = 0, (D[1](V))(0, theta) = 0, V(1, theta) = 0, (D[1](V))(1, theta) = 0


W(0, theta) = 0, (D[1](W))(0, theta) = 0, W(1, theta) = 0, (D[1](W))(1, theta) = 0




Download fem2




I'm working towards creating a way to visualise real polynomial ideals! (or at least the solutions of the polynomials in the ideals) this code creates a plot showing the solutions to all the polynomials in the ideal generated by P1 and P2 (these are specified in the code)

P1 := x^2+2*y^2-3;
solve(P1, y);
Plot1 := plot([%], x = -2 .. 2);

P2 := -2*x^2+2*x*y+3*y^2+x-4;
solve(%, y);
Plot2 := plot([%], x = -4 .. 2);

solve(%, y);
seq(plot([%], x = -4 .. 2), a = 0 .. 10, .1);
display(%, Plot1, Plot2)

This is because when you multiply two polynomials their set of solution curves is just the union of the sets of curves associated with the previous polynomials.

For the next step I'd like to create a graph of the solutions associated with an ideal with three generators. To stop this from being excessively messy I'd like to do it with the RGB value of the colour of a curve is determined by  a and b where the formula for a generic polynomial that we are solving and graphing is given by:


where P3 is given by

P3 := x*y-3

I've tried various ways to use cury to make this work (my intuition is cury is the right function to use here)  but got no where. Any ideas how to procede?

Which sorting related with famous sequence

for example 

sorting differential equation in a list

then access the list with famous sequence as index such as using https://oeis.org/

after access with sequence as index, use choose function to get combinations then most result are isomorphism differential ideals?

is there methods about this sorting in Richard Stanley Combinatiric book? which page of it?

Last month I still can read file


read “c://Users//hello//Documents//h.m”


now it return error

no read access c://Users//hello//Documents/


in security I add the m file into readable 

I saw open file at c drive has many shell folders 

i just add m file

but still the same error

i unencrypted m file by window properties

still the same error

i save file into maple roaming directory under 12 folder , still the same error

i save into maple installation directory maple 12 , still the same error

possible to solve following equation with unknown parameter omega.

parameter constant.

I see before for one dimension ode this type equation was solved.

Now for 2d equation is possible?

can consider or I can send again.




Why am I not able to use my MaplePrimes login credentials to login into MapleCloud?

A few months ago i completely lost one of my linux operating systems in a single line of commands I entered into the terminal, and at some point I want to utilize the StringTools package with commands like  RegSubs and RegMatch to output the matching strings that match for the current command line content in a linux terminal, so I will know before I hit the enter key how stupid it was of me to do so *prior* to hitting the enter key.


The part I have no idea about is the piping of the keyboard input  for a terminal window to the maple session that will output the strings matching as previously described. I'm sorry if this question is not very clear I will try clarify more this afternoon. 



I have the following PDE



My Question: I have done manually following calculations. I want to verify the following operations are right, or not by MAPLE. Could you help me, please?



Suppose that


In here,  is an Nx1 matrix, P, C are NxN matrices. (N is an integer and superscript T   denotes the transpose of the matrix.)  and P are given matrices. But the matrix C is ungiven I will find it in the final step. But my question doesn' t include all steps. I just wonder how to calculate the first two steps by Maple.


( If Maple doesn' t do matrix algebra, we can treat them as if , P, C were not matrix. I think the result won' t be changed. We will get again equation 9 by Maple.)

First Step

We will find the followings 


 in terms of the matrices  ,  P and C.

So, if we integrate Equation (2) with respect to x (from 0 to x), and  by using the following two assumptions


we have 


substituting x=1  in Equation (3)


if rewrite Eqn. (4), we have


substituting Eqn. (5) to Eqn. (3), we have 


integrating Equation (3) with respect to t,

we have 


If we integrate Equation (2) from 0 to x with respect to t, we have


Second Step We will substitute the terms to the pde ( Equation 1)

Substituting Eqn. (6), (7), (8) to Eqn. (1), we have finally


I want to do the above calculations by Maple.  

Because I have more complex questions than above, I want to write a Maple code in order to avoid calculation errors.  

Final Step for curious: it's hard to explain the whole method here. Briefly, we will discretize equation 9 for some collocation points t and x. And after doing it, we will have a system of an algebraic equation. (N equation and N unknown ( C is Nx1 unknown vector to be find) )

And then we will substitute vector C to Eqn. 7

Code for Matrices , P^1, P^2,etc.


Best Regards...

maple does not work at all

it displays this error

Error, (in StringTools:-FormatMessage) unknown option MAPLE

Generally when I respond to questions on this site, I make sure that I tick the checkbox requesting that I get an email when updates are made to the thread.

I've just realised that I have been receiving no such updates for a week or so. Two possibilities

  1. Problem with Mapleprimes website, meaning that email updates aren't being generated/sent
  2. Problem with my ISP

Before I try investigating (2) above, I'd just like to know if anyone else has seen any issue which might be explained by (1) above

How to calculate potential function of Maxwell equations?

is there calculation examples of strong and weak force examples too?

which library can calculate intersection numbers of familes of potential function of Maxwell equations?

is there any examples?

Hi everybody:

I have the code in Maple that when run it I see this error, how can I solve this error? 



hello everyone,

please I need our help to find the eigenvalues (m) of this equation (eq)

thank you 






Digits := 5:



eq := exp(-m*xi)*(exp((1/4)*sqrt(-m)*r*(r-1))*(1+(7/20)*sqrt(m)*r+((49/800)*m-(1/4)*sqrt(m))*r^2)*r^I+exp((1/4)*sqrt(-m)*r*(r-1))*(1+(7/20)*sqrt(m)*r+((49/800)*m-(1/4)*sqrt(m))*r^2)*r^I*cos(theta)+r^I*sin(5*theta))





Download eq.mw


Hi all

trying to find analytically sin(erf(t)) and cos(erf (t)) rather than numerically


Error, numeric exception: division by zero
            0, "numeric exception: division by zero"
lastexception; # ???
            Typesetting:-Typeset, "invalid input: %1 expects %2 arguments, but received %3", type, 2, 3


So, printing lastexception produces a new error!
When typesetting=standard, it's OK.


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