Maple 2021 Questions and Posts

These are Posts and Questions associated with the product, Maple 2021

I am a new user to Maple, but have used PTC's Mathcad and Prime.

I have several matrices that I need to combine both vertically and horizontally.  The command augment will combine the matrices horizontally.  I was unable to find a command to combine the matrices vertically.  I tried the stack command (Prime command).  The Maple stack command appears to have a different functionality.  Could you suggest which command would do the job?  The matrices are large and I would like to limit the number of rows and columns shown in the document.

The next step will be sorting the data. I am researching this at this time.

Thank you for the support,

David Tietje

When I added kernelopts('assertlevel'=2): now Maple gives an error from call to solve. Also PDEtools:-Solve  gives same error. 

If I remove the  kernelopts('assertlevel'=2): it works OK and gives solution.

Is this known issue? I'd like to keep kernelopts('assertlevel'=2): and still use solve. Maple 2021.2 on windows 10

interface(version);

`Standard Worksheet Interface, Maple 2021.2, Windows 10, November 23 2021 Build ID 1576349`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1131 and is the same as the version installed in this computer, created 2022, January 7, 9:5 hours Pacific Time.`

restart;

3

eq:=1/8*2^(1/2)*(-2*x*(w^4*x^11+(4*w^4-6*w^3)*x^10+(10*w^4-22*w^3+17*w^2)*x^9+(16*w^4-50*w^3+62*w^2-30*w)*x^8+(71/2+19*w^4-72*w^3+132*w^2-114*w)*x^7+(140-685/3*w+16*w^4-76*w^3+176*w^2)*x^6+(263-841/3*w+10*w^4-56*w^3+331/2*w^2)*x^5+(292-1385/6*w+105*w^2+4*w^4-30*w^3)*x^4+(821/4+w^4-733/6*w-10*w^3+91/2*w^2)*x^3+(173/2-2*w^3-122/3*w+11*w^2)*x^2+(77/4+3/2*w^2-37/6*w)*x+3/2-1/2*w)*(-1+I*3^(1/2))^(1/2)+2^(1/2)*(I*x*(w^4*x^11+(4*w^4-6*w^3)*x^10+(10*w^4-22*w^3+17*w^2)*x^9+(16*w^4-50*w^3+62*w^2-30*w)*x^8+(71/2+19*w^4-72*w^3+132*w^2-114*w)*x^7+(140-685/3*w+16*w^4-76*w^3+176*w^2)*x^6+(263-841/3*w+10*w^4-56*w^3+331/2*w^2)*x^5+(292-1385/6*w+105*w^2+4*w^4-30*w^3)*x^4+(821/4+w^4-733/6*w-10*w^3+91/2*w^2)*x^3+(173/2-2*w^3-122/3*w+11*w^2)*x^2+(77/4+3/2*w^2-37/6*w)*x+3/2-1/2*w)*3^(1/2)-1/4-3*w^4*x^12+(-12*w^4+10*w^3)*x^11+(-30*w^4+26*w^3-7*w^2)*x^10+(-48*w^4+54*w^3+14*w^2-14*w)*x^9+(63/2-57*w^4+64*w^3+36*w^2-98*w)*x^8+(140-48*w^4+68*w^3+80*w^2-565/3*w)*x^7+(255-769/3*w-30*w^4+48*w^3+127/2*w^2)*x^6+(292-1169/6*w-12*w^4+34*w^3+45*w^2)*x^5+(797/4-661/6*w+7/2*w^2-3*w^4+14*w^3)*x^4+(173/2-80/3*w+6*w^3-w^2)*x^3+(69/4-25/6*w-9/2*w^2)*x^2+(3/2+3/2*w)*x))/(x^2+x+1)^4/x^4;

(1/8)*2^(1/2)*(-2*x*(w^4*x^11+(4*w^4-6*w^3)*x^10+(10*w^4-22*w^3+17*w^2)*x^9+(16*w^4-50*w^3+62*w^2-30*w)*x^8+(71/2+19*w^4-72*w^3+132*w^2-114*w)*x^7+(140-(685/3)*w+16*w^4-76*w^3+176*w^2)*x^6+(263-(841/3)*w+10*w^4-56*w^3+(331/2)*w^2)*x^5+(292-(1385/6)*w+105*w^2+4*w^4-30*w^3)*x^4+(821/4+w^4-(733/6)*w-10*w^3+(91/2)*w^2)*x^3+(173/2-2*w^3-(122/3)*w+11*w^2)*x^2+(77/4+(3/2)*w^2-(37/6)*w)*x+3/2-(1/2)*w)*(-1+I*3^(1/2))^(1/2)+2^(1/2)*(I*x*(w^4*x^11+(4*w^4-6*w^3)*x^10+(10*w^4-22*w^3+17*w^2)*x^9+(16*w^4-50*w^3+62*w^2-30*w)*x^8+(71/2+19*w^4-72*w^3+132*w^2-114*w)*x^7+(140-(685/3)*w+16*w^4-76*w^3+176*w^2)*x^6+(263-(841/3)*w+10*w^4-56*w^3+(331/2)*w^2)*x^5+(292-(1385/6)*w+105*w^2+4*w^4-30*w^3)*x^4+(821/4+w^4-(733/6)*w-10*w^3+(91/2)*w^2)*x^3+(173/2-2*w^3-(122/3)*w+11*w^2)*x^2+(77/4+(3/2)*w^2-(37/6)*w)*x+3/2-(1/2)*w)*3^(1/2)-1/4-3*w^4*x^12+(-12*w^4+10*w^3)*x^11+(-30*w^4+26*w^3-7*w^2)*x^10+(-48*w^4+54*w^3+14*w^2-14*w)*x^9+(63/2-57*w^4+64*w^3+36*w^2-98*w)*x^8+(140-48*w^4+68*w^3+80*w^2-(565/3)*w)*x^7+(255-(769/3)*w-30*w^4+48*w^3+(127/2)*w^2)*x^6+(292-(1169/6)*w-12*w^4+34*w^3+45*w^2)*x^5+(797/4-(661/6)*w+(7/2)*w^2-3*w^4+14*w^3)*x^4+(173/2-(80/3)*w+6*w^3-w^2)*x^3+(69/4-(25/6)*w-(9/2)*w^2)*x^2+(3/2+(3/2)*w)*x))/((x^2+x+1)^4*x^4)

solve(eq = 0,w)

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

PDEtools:-Solve(eq=0,w)

w = (1/2)*(2*x^2+1)/((x^2+x+1)*x)

restart;

interface(warnlevel=4);
kernelopts('assertlevel'=2):

3

eq:=1/8*2^(1/2)*(-2*x*(w^4*x^11+(4*w^4-6*w^3)*x^10+(10*w^4-22*w^3+17*w^2)*x^9+(16*w^4-50*w^3+62*w^2-30*w)*x^8+(71/2+19*w^4-72*w^3+132*w^2-114*w)*x^7+(140-685/3*w+16*w^4-76*w^3+176*w^2)*x^6+(263-841/3*w+10*w^4-56*w^3+331/2*w^2)*x^5+(292-1385/6*w+105*w^2+4*w^4-30*w^3)*x^4+(821/4+w^4-733/6*w-10*w^3+91/2*w^2)*x^3+(173/2-2*w^3-122/3*w+11*w^2)*x^2+(77/4+3/2*w^2-37/6*w)*x+3/2-1/2*w)*(-1+I*3^(1/2))^(1/2)+2^(1/2)*(I*x*(w^4*x^11+(4*w^4-6*w^3)*x^10+(10*w^4-22*w^3+17*w^2)*x^9+(16*w^4-50*w^3+62*w^2-30*w)*x^8+(71/2+19*w^4-72*w^3+132*w^2-114*w)*x^7+(140-685/3*w+16*w^4-76*w^3+176*w^2)*x^6+(263-841/3*w+10*w^4-56*w^3+331/2*w^2)*x^5+(292-1385/6*w+105*w^2+4*w^4-30*w^3)*x^4+(821/4+w^4-733/6*w-10*w^3+91/2*w^2)*x^3+(173/2-2*w^3-122/3*w+11*w^2)*x^2+(77/4+3/2*w^2-37/6*w)*x+3/2-1/2*w)*3^(1/2)-1/4-3*w^4*x^12+(-12*w^4+10*w^3)*x^11+(-30*w^4+26*w^3-7*w^2)*x^10+(-48*w^4+54*w^3+14*w^2-14*w)*x^9+(63/2-57*w^4+64*w^3+36*w^2-98*w)*x^8+(140-48*w^4+68*w^3+80*w^2-565/3*w)*x^7+(255-769/3*w-30*w^4+48*w^3+127/2*w^2)*x^6+(292-1169/6*w-12*w^4+34*w^3+45*w^2)*x^5+(797/4-661/6*w+7/2*w^2-3*w^4+14*w^3)*x^4+(173/2-80/3*w+6*w^3-w^2)*x^3+(69/4-25/6*w-9/2*w^2)*x^2+(3/2+3/2*w)*x))/(x^2+x+1)^4/x^4:

solve(eq = 0,w)

Error, (in Internal:-FactorEasy) assertion failed, Internal:-FactorEasy expects its return value to be of type list(_POWER(POLYNOMIAL, posint)), but computed [_POWER(POLYNOMIAL([0, [z, x, r1, r2, r3], [[[[1], [0, -1]], 0, [[1]]], [[1], 0, [1]], [-3, 0, 1]]], [[[0, [[1]]]]]), 1), _POWER(POLYNOMIAL([0, [z, x, r1, r2, r3], [[[[1], [0, -1]], 0, [[1]]], [[1], 0, [1]], [-3, 0, 1]]], [[[[0, [1]]]]]), FAIL), _POWER(POLYNOMIAL([0, [z, x, r1, r2, r3], [[[[1], [0, -1]], 0, [[1]]], [[1], 0, [1]], [-3, 0, 1]]], [[[[[0, 1]]]]]), FAIL), _POWER(POLYNOMIAL([0, [z, x, r1, r2, r3], [[[[1], [0, -1]], 0, [[1]]], [[1], 0, [1]], [-3, 0, 1]]], [[[[[-1], [0, 1]]], 0, [[[-8], [0, 8]]], 0, [[[-24], [0, 24]]], 0, [[[-32], [0, 32]]], 0, [[[-16], [0, 16 ... , [[[-160], [0, 160]]], [[[-64], [0, 64]]], [[[-16], [0, 16]]]]]), 1)]

PDEtools:-Solve(eq=0,w)

Error, (in Internal:-FactorEasy) assertion failed, Internal:-FactorEasy expects its return value to be of type list(_POWER(POLYNOMIAL, posint)), but computed [_POWER(POLYNOMIAL([0, [z, x, r1, r2, r3], [[[[1], [0, -1]], 0, [[1]]], [[1], 0, [1]], [-3, 0, 1]]], [[[0, [[1]]]]]), 1), _POWER(POLYNOMIAL([0, [z, x, r1, r2, r3], [[[[1], [0, -1]], 0, [[1]]], [[1], 0, [1]], [-3, 0, 1]]], [[[[0, [1]]]]]), FAIL), _POWER(POLYNOMIAL([0, [z, x, r1, r2, r3], [[[[1], [0, -1]], 0, [[1]]], [[1], 0, [1]], [-3, 0, 1]]], [[[[[0, 1]]]]]), FAIL), _POWER(POLYNOMIAL([0, [z, x, r1, r2, r3], [[[[1], [0, -1]], 0, [[1]]], [[1], 0, [1]], [-3, 0, 1]]], [[[[[-1], [0, 1]]], 0, [[[-8], [0, 8]]], 0, [[[-24], [0, 24]]], 0, [[[-32], [0, 32]]], 0, [[[-16], [0, 16 ... , [[[-160], [0, 160]]], [[[-64], [0, 64]]], [[[-16], [0, 16]]]]]), 1)]

 

Download assertion_failed.mw

A user would like to know if it is possible to specify a data set say, x:=[1,2,3,4,5,6] and then extract a random sample from that data set, i.e. xsample:=[3,2,4] for a bootstrapping-type calculation.

We suggested they use something like the following:

restart; with(Statistics); my_data := [1, 2, 4, 5.5, 5.5, 6]; X := RandomVariable(EmpiricalDistribution(my_data)); s := Sample(X, 10); Bootstrap(Mean, X, samplesize = 4, replications = 10000)

HFloat(3.9984625)

(1)

NULL

Download array-random-sample.mw

Hello people in Mapleprimes,
I haven't written in this site for a long time.

I have a question in the below program, which is to write ribbons.
For the implementation of this program, 
I wrote this.
ribbonplot5([cos, sin, cos + sin], -Pi .. Pi,numpoints=20);

In the part of pattern matching, as -Pi .. Pi above is a range, so it is OK.
But, when I changed this part to x=-Pi..Pi, an error message appears.

ribbonplot5([cos, sin, cos + sin],x=-Pi .. Pi,numpoints=20);

brings error messages:
"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"

In the code of ribbonplot5,  x=-Pi..Pi which is the type of name=range shoud satisfy the pattern matching, as I wrote in the first part of the program as 
ribbonplot5 := proc(Flist, r1::{range,name=range})

I cannot know why the part of the program:
 
" else
       newFlist := map(unapply, Flist, lhs(r1));
     opts := ['labels'=[lhs(r1), " "," "],
                 args[3 .. nargs]];
    ribbonplot5(newFlist,rhs(r1),op(opts)):
"

wouldn't work well.

I wish I could get an answer to this. 

Thanks in advance.

This is a program in maple9 Advanced Programming Gude p. 253

graphic_ribbonplot.mw

restart;
extend := proc(f)
     local x, y;
     unapply(f(x), x, y);
end proc:
p:=x->cos(2*x):
q:=extend(p);


ribbonplot5 := proc(Flist, r1::{range,name=range})
     local i, m, p, n, opts,newFlist;
     opts := [args[3 .. nargs]];
     if type(r1, range) then
         if not hasoption(opts, 'numpoints', 'n', 'opts')
         then n := 25
         end if; 
         m := nops(Flist);
         p := seq(plot3d(extend(Flist[i]), r1, (i-1) .. i,
                                  grid=[n, 2], op(opts)),
                       i = 1 .. m):
         plots[display](p):
     else
       newFlist := map(unapply, Flist, lhs(r1));
     opts := ['labels'=[lhs(r1), " "," "],
                 args[3 .. nargs]];
    ribbonplot5(newFlist,rhs(r1),op(opts)):
   end if:
end proc:
ribbonplot5([cos, sin, cos + sin], -Pi .. Pi,numpoints=20);

I'd like to get the simplest possible expression when using simplify. The problem is that this is all done in a program, without having the benifit of looking at the expression on the screen and trying things. So I need a method that works for large set of input all the time.

I noticed in this example that simplify did not do what I think it should have.

Given the expression -2*(x^3 + 2)/(x*(x + 1)*(sqrt(3)*I + 2*x - 1)*(sqrt(3)*I - 2*x + 1)) it can be simplified to (x^3 + 2)/(2*x^4 + 2*x) but  I had to go into many tries in order to get this final result.

Is there a better way to do this? I end up now   doing simplify(expand(numer(expr))/expand(denom(expr))) in the hope to get better simplification.  Here is an example


 

interface(version);

`Standard Worksheet Interface, Maple 2021.2, Windows 10, November 23 2021 Build ID 1576349`

restart;

w:=-2*(x^3+2)/x/(x+1)/(I*3^(1/2)+2*x-1)/(I*3^(1/2)-2*x+1);

-2*(x^3+2)/(x*(x+1)*(I*3^(1/2)+2*x-1)*(I*3^(1/2)-2*x+1))

simplify(w)

(-2*x^3-4)/(x*(x+1)*(I*3^(1/2)+2*x-1)*(I*3^(1/2)-2*x+1))

simplify(evalc(w))

(1/2)*(x^3+2)/((x^2-x+1)*(x+1)*x)

simplify(w) assuming x::real

(-2*x^3-4)/(x*(x+1)*(I*3^(1/2)+2*x-1)*(I*3^(1/2)-2*x+1))

simplify(w,size)

(-2*x^3-4)/(x*(x+1)*(I*3^(1/2)+2*x-1)*(I*3^(1/2)-2*x+1))

simplify(w,symbolic)

(-2*x^3-4)/(x*(x+1)*(I*3^(1/2)+2*x-1)*(I*3^(1/2)-2*x+1))

simplify(w,sqrt)

(-2*x^3-4)/(x*(x+1)*(I*3^(1/2)+2*x-1)*(I*3^(1/2)-2*x+1))

simplify(expand(numer(w))/expand(denom(w)))

(x^3+2)/(2*x^4+2*x)


It would be nice if Maple simplify would just do it directly as follows in Mathematica. May be there is a an  option I am overlooking

 

Download simplify.mw

I drew a methane molecula and display three times because I wanted to get two-fold and three-fold symmetry axis. ,I would is that I would like to get a more exact output and doing it without clicking, it's say, using code. Can someone help me?tareaclase6.mw
 

University of Costa Rica 

Course: SP-1493

Student: Lic. Marcus Vinicio Mora Salas

Instructor: Dr. Erick Castellón Elizondo

 

Assigment5

Description

 

In this assigment exercises e2.113,  e2.114, e2.115 and e2.117 was solved.

NULL

***e2.113

   

 

 

 

NULL


 

Download tareaclase6.mw

 

Suppose I have a real function which is defined on these intervals [x0,x1],...[x1,xn], and on each interval it's defined differently, for example f(x):=sqrt(x) if x>=0; f(x):=1/x if x<0.

For the last example I tried my last resort to use the assuming operator the following way:

f := ((x -> sqrt(x)) assuming (0 <= x)) or ((x -> 1/x) assuming (x < 0)) plot(f, x)

But it doesn't seem to be working, how do you propose to define this function? perhaps proc?

I tried looking for an example in maple's help, but didn't find any.

Your help is appreciated.

I read that abs(v) should find the magnitude of complex number. But I find cases where it does not.

Should one then use sqrt( Re(v)^2 + Im(v)^2 ) instead or is there different command to use?  Here is an example

interface(version)

`Standard Worksheet Interface, Maple 2021.2, Windows 10, November 23 2021 Build ID 1576349`

restart;

v:=1/16*(I*5^(1/2)+I-4*sin(1/5*Pi))*2^(3/10)*(5-5^(1/2))^(1/2)-1/8*2^(4/5)*((I*5^(1/2)+I)*sin(1/5*Pi)+1/2*5^(1/2)+3/2)

(1/16)*(I*5^(1/2)+I-4*sin((1/5)*Pi))*2^(3/10)*(5-5^(1/2))^(1/2)-(1/8)*2^(4/5)*((I*5^(1/2)+I)*sin((1/5)*Pi)+(1/2)*5^(1/2)+3/2)

abs(v)

-(1/16)*(I*5^(1/2)+I-4*sin((1/5)*Pi))*2^(3/10)*(5-5^(1/2))^(1/2)+(1/8)*2^(4/5)*((I*5^(1/2)+I)*sin((1/5)*Pi)+(1/2)*5^(1/2)+3/2)

sqrt( Re(v)^2 + Im(v)^2 );

((-(1/4)*2^(3/10)*(5-5^(1/2))^(1/2)*sin((1/5)*Pi)-(1/8)*2^(4/5)*((1/2)*5^(1/2)+3/2))^2+((1/16)*2^(3/10)*(5-5^(1/2))^(1/2)*(5^(1/2)+1)-(1/8)*2^(4/5)*(5^(1/2)+1)*sin((1/5)*Pi))^2)^(1/2)

 

Download complex.mw

Here is the same thing in Mathematica:

I searched help for modulus but could not find one.

Maple 2021.2

question8.mw

In the exercise uploaded I have to plot asymptotes of a function. I know this is possible using definitions of all kind of asymptotes and ploting in a figure. However I would like to know if exists some parameter for plot method that automatically show asymptotes.

question7.mw

NULL

***e2.106

 

Plot this couple of parametric equations, identify the geometric figure known as the folium of Descartes , and relate properties of the figure to numerical coefficients in the equations.

  x = 3*t/(t^3+1), y = 3*t^2/(t^3+1)   

NULL

restart: with(plots):

 

 

 

See how the plot of the folium of Descartes can be built with the following code:

d1 :=

Error, invalid terms in product: -10 .. 10

Error, invalid terms in product: -10 .. 10

Error, (in plots:-pointplot) points cannot be converted to floating-point values

NULL

NULL

Download question7.mw

For this question I need that who help me focus in second block of code in the document. Basically, what I am trying is to get a plot of folium of Dercastes using parametric equation to plot ordered pairs. In order to success, is needed to exclude t=-1. In the block is showed what I tried. I concluded that my approach in solving that part of exercise is wrong. What could be a well approach?

question6.mw
How you can see, in the following exercise I built five plots, every one with the graph of two functions. The exersise say that I must find coordinates of any intersection. I think I can do it with solve command. However, I want point out coordinates of  intersections inside the plots. Probably exists a command or a parameter to success with my objetive. How can I do it?

NULL

*** e2.103

 

Plot the following couples of formulae; note in particular the contrasting forms of two curves in each case, and find the coordinates of any intersections.

i)    {x, x^3},

ii)    {x^2, x^4},

iii)    {1/x, 1/x^2},

 iv)   {x^2, sqrt(x)},

 v)   {x^3, abs(x^(1/3))}

 

restart:

NULL

Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Salas;
Chemist;
Postgraduate student at University of Costa Rica;

Download question6.mw

question5.mw

In document uploaded I tried to write a code to get as output 11 plots. I would like a format as this: 9 plots in 3 columns an 3 rows, and a fourth row with two center plots. To explain me better, I drew a rustic sketch of what I want, basically something like this:

However I tried but I fail and my output is horrible. So, I want to ask: Does exists some option to the plot[display] command or should I try another aproach?

Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Salas;
Chemist;
Postgraduate student.

As part of my course work I've encountered a block wherein I need to convert a 4th order TF to a SmithForm but am unable to do so.

Can anyone help me with the code as attatched.

A := Matrix([[(.3384*x^3-26.13*x^2-.3659*x+0.1678e-1)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598), (.4755*s^3-25.3*s^2-51.36*s-1.387)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598)], [(-.3349*s^3+18.21*s^2+.3487*s-0.5939e-1)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598), (-.3107*s^3+17.81*s^2+35.49*s+1.027)/(s^4+3.068*s^3-3.362*s^2-.5748*s+.7598)]])

Matrix(%id = 36893488152131246308)

(1)

"->"

Error, (in gcdex) invalid arguments

 

"->"

SmithForm(Matrix(%id = 36893488152131266788))``

(2)

with(LinearAlgebra)

NULL

S := SmithForm(A, s)

Error, (in gcdex) invalid arguments

 

with(LinearAlgebra); A := Matrix([[1, 2*x, 2*x^2+2*x], [1, 6*x, 6*x^2+6*x], [1, 3, x]])

Matrix(%id = 36893488152361731844)

(3)

S := SmithForm(A, x)

Matrix(%id = 36893488152348668020)

(4)

NULL

Download SmithForm.mw

This is a simple problem of Chemistry. I solved the exercise, but there are three aspects I don't like about output:
1) Even kg*m2 *s-2 = J (SI unit to energy) and both are correct, one must be explicit with units in order to be totally clear, so I need an output with units of J/mol and not kg*m2 *s-2 mol-1.
2) I had to hardcode number of significant figures, so I had to analize quantitys in order to determine this number, wich as you can see, is three. I think Maple can compute significant figures automatically, but I could not find the command in documentation and even in this case is not totally needed, I would like to learn how do it because it could be very useful for more complex expressions.
3) Finally, output must be expressed using scientific notation, it's say enthalpy = 10.4*104 J/mol.
Therefore: How can I get adecuate output?
Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Sallas;
Chemist;
Postgraduate student. question4.mw

*** e1.501

 

Using this equation attributed to Clausius and Clapeyron,

ln(P[2]/P[1]) = Delta*H[vap]/R 1/T[1]-1/T[2]

and these data for the vapour pressure of liquid mercury at the indicated temperatures,

      P =  1.6 10^(-4) Pa at T = 273.15 K and P = 36.4 Pa at T = 373.15 K

estimate the enthalpy change Delta*H[vap] for vapourization of mercury over this range of temperature.

 

p := [1.6e-4*Unit('Pa'), 36.4*Unit('Pa')]:

Delta(H[vap]) = 0.105e6*Units:-Unit(m^2*kg/(s^2*mol*K))*Units:-Unit(K)

``

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system_of_PDE.mw

NULL

NULL

Digits := 30; with(PDEtools); with(plots); Ops1 := numpoints = 100; Ops2 := color = magenta; Ops3 := color = blue; Ops4 := color = "BlueViolet"; Ops5 := axes = boxed, shading = zhue, orientation = [40, 50]; a := 0; b := 1; Tf := .5

axes = boxed, shading = zhue, orientation = [40, 50]

 

.5

(1)

E := 1480

1480

(2)

Ebes := 5990

5990

(3)

n0 := 900000

900000

(4)

ro := 1200

1200

(5)

m := 12.6

12.6

(6)

f := sig(x, t)-Ebes*`&varepsilon;ij`(x, t)

sig(x, t)-5990*`&varepsilon;ij`(x, t)

(7)

n := 900000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m)

900000*exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))

(8)

NULL

P := 5

5

(9)

w := 4

4

(10)

k := 7

7

(11)

i := 5

5

(12)

eq1 := diff(sig(x, t), x, x) = ro*(diff(sig(x, t), x, x))/E+ro*(diff(sig(x, t), t)-Ebes*f/(9000000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m)))*(1+f/m)/(9000000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m))

diff(diff(sig(x, t), x), x) = (30/37)*(diff(diff(sig(x, t), x), x))+(1/7500)*(diff(sig(x, t), t)-(599/900000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t)))*(1+0.793650793650793650793650793651e-1*sig(x, t)-475.396825396825396825396825397*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))

(13)

 

eq2 := diff(`&varepsilon;ij`(x, t), t) = f/(9000000*exp(-(sig(x, t)-E*`&varepsilon;ij`(x, t))/m))

diff(`&varepsilon;ij`(x, t), t) = (1/9000000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))

(14)

NULL

sys := {eq1, eq2}

{diff(diff(sig(x, t), x), x) = (30/37)*(diff(diff(sig(x, t), x), x))+(1/7500)*(diff(sig(x, t), t)-(599/900000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t)))*(1+0.793650793650793650793650793651e-1*sig(x, t)-475.396825396825396825396825397*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t)), diff(`&varepsilon;ij`(x, t), t) = (1/9000000)*(sig(x, t)-5990*`&varepsilon;ij`(x, t))/exp(-0.793650793650793650793650793651e-1*sig(x, t)+117.460317460317460317460317460*`&varepsilon;ij`(x, t))}

(15)

NULL

IBC1 := {sig(0, t) = P*sin(w*k*i), sig(10, t) = P*sin(w*k*i), sig(x, 0) = 0, sig(x, 1) = 0, `&varepsilon;ij`(x, 0) = 0}

{sig(0, t) = 5*sin(140), sig(10, t) = 5*sin(140), sig(x, 0) = 0, sig(x, 1) = 0, `&varepsilon;ij`(x, 0) = 0}

(16)

S := 1/100; Ops := spacestep = S, timestep = S; Sol1 := pdsolve(sys, IBC1, [sig, `&varepsilon;ij`], numeric, time = t, range = a .. b, Ops)

1/100

 

spacestep = 1/100, timestep = 1/100

 

Error, (in pdsolve/numeric) unable to handle elliptic PDEs

 

``

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