## Why dchange is not working in this example?...

Asked by:

I haven't soved yet why dchange is not working for this simple command. Any help out there?

Thanks a lot

## Problem aplying the chain rule with dchange...

Asked by:

I have a problem using dchange when my variable depend on two (or more variables) and I would like to apply the chain rule.

For example, when I use the command

I would expect something like

But I get an error saying that the number of new variables and transformation equations must be the same.

Any idea how I could solve it?

Thanls a lot for your help.

## The dchange command returns zero...

Asked by:

Hello Maple primers

I am trying to do a coordinate transformation which involves a number of partial derivatives. I turned to the PDETools[dchange] to accomplish this but it will just return 0 when run through.

The problem is as such. First two functions are defined which contain a lot of "stuff". Then the forward and reverse transformations are defined between the coordinates; and finally the transformation is done.

del_1:=Diff(Y,r1,r1)+2/r1*(Diff(Y,r1)) + Diff(Y,r2,r2)+2/r2*(Diff(Y,r2))+2*(Diff(Y,r3,r3))+4/r3*(Diff(Y,r3))+((r1^2-r2^2+r3^2)/(r1*r3))*(Diff(Y,r1,r3))+(r2^2-r1^2+r3^2)/(r2*r3)*(Diff(Y,r2,r3)):

del_2:=Diff(Y,r1,r1)+2/r1*(Diff(Y,r1))+(r1^2-r2^2+r3^2)/(r1*r3)*Diff(Y,r1,r3)+Diff(Y,r2,r2)+2/r2*(Diff(Y,r2))+(-r1^2+r2^2+r3^2)/(r2*r3)*(Diff(Y,r2,r3))+4/r3*(Diff(Y,r3))+2*(Diff(Y,r3,r3)):

#Forward transformation

R1:=0.5*(v)+0.25*(w):
R2:=0.5*(u)+0.25*(w):
R3:=0.5*(u)+0.5*(v):

tr:={r1=R1,r2=R2,r3=R3}:

#Reverse transformation
rR1:=(-r1+r2+r3):
rR2:=(r1-r2+r3):
rR3:=2*(r1+r2-r3):

rtr:={u=rR1,v=rR2,w=rR3}:
nv:={u,v,w}:
AA:=simplify(del_1+del_2);
PDEtools[dchange](tr,AA,nv,rtr);

This will return zero. Is there something obvious I am missing here? I have used the dchange tool before in a similar manner and it has worked without issue.

## Solving PDE with variable change...

Asked by:

I'm trying to solve a beam vibration problem. I am relatively new to Maple and trying to solve PDE's. I feel like I'm pretty close, but I don't understand what's wrong here.

This is my maple file.

Thesis_Pde2_attempt.mw

as a note, I made some simplifying assumptions. I am just using part of this equation since it is less complex. And my boundary conditions are simply supported on both ends so no displacement and no 2nd derivative at the ends.

Any help would be greatly appreciated!!

## Variable change in PDE...

Asked by:

Hello All,

I am doing research for my master's thesis and I am trying to type a PDE into maple and have been struggling for about 2 weeks now. I am new to Maple but have had a lot of Matlab experience. I've seen a couple of ways to do variable changes and things but I'm still.

These are the substitutions I'm trying to do.

into this equation, but and some of these terms are 0 (x*d/dt are 0, P, and M_e, and q_ye).

So it is basically a Euler-Bernoulli beam with a free vibration.

I tried to use dchange to do the substitutions but I am having trouble defining ...

or doing both

I see why there is an error but I don't know how to fix it.

I've also tried

Which is close but still doesn't look quite right. because d/dt(omega*t/2) -> omega/2

Any thoughts?

Thanks in advance

## An issue with Physics[Vectors] in Maple 17...

Asked by:

I am having an issue with Physics[Vectors] in Maple 17, specifically an interference with PDEtools:-dchange. My apologies, this post is lengthy & a bit messy. I did upload a worksheet with the code; link at the end. The upload exhibits the UNWANTED behaviour in Maple 17.

Here are a few lines of code that exhibit the WANTED behaviour (change of variable and solving a de). it is run in Maple17 with Physics loaded but NOT Physics[Vectors]. The paste into Mapleprimes looks too messy to be useful so I am just showing the relevant lines; the file has everything:

-(diff(E1_(x, y, z, t), x, x))-(diff(E1_(x, y, z, t), y, y))-(diff(E1_(x, y, z, t), z, z)) = -mu*epsilon*(diff(E1_(x, y, z, t), t, t));

PDEtools:-dchange({x = r*cos(theta), z = r*sin(theta)}, -(diff(diff(E1_(x, y, z, t), x), x))-(diff(diff(E1_(x, y, z, t), y), y))-(diff(diff(E1_(x, y, z, t), z), z)) = -mu*epsilon*(diff(diff(E1_(x, y, z, t), t), t)), simplify);

subs(E1_(r, theta, y, t) = R(r)*exp(I*(-k*y+omega*t)), -((diff(diff(E1_(r, theta, y, t), y), y))*r^2+(diff(diff(E1_(r, theta, y, t), r), r))*r^2+(diff(E1_(r, theta, y, t), r))*r+diff(diff(E1_(r, theta, y, t), theta), theta))/r^2 = -mu*epsilon*(diff(diff(E1_(r, theta, y, t), t), t)));

dsolve((5));

So far this is all as expected.

Now I rerun this thing with Physics[Vectors] loaded rather than just Physics. Everything looks the same until I get to the line starting with subs(E1_ :

subs(E1_(r, theta, y, t) = R(r)*exp(I*(-k*y+omega*t)), -((diff(diff(E1_(r, theta, y, t), y), y))*r^2+(diff(diff(E1_(r, theta, y, t), r), r))*r^2+(diff(E1_(r, theta, y, t), r))*r+diff(diff(E1_(r, theta, y, t), theta), theta))/r^2 = -mu*epsilon*(diff(diff(E1_(r, theta, y, t), t), t)));

plus many more lines of expressions. I am not sure what is going wrong; but after the dchange the code behaves funky: I have had simplify producing similarly weird expressions etc.

Note that on Maple 15 this all works as expected and no issues show up for me. If the version of Physics I have on Maple 17.02 is bad; how do I change that? (I have not tried to update Physics separately, and it isn't obvious to me where to find it for Maple 17). It is sort-of an issue as I want to use this as a demo for students, who in fact will be running Maple 18... but I am stuck at 17 (and often using 15 at home) so I need this to work there (17), too.

TIA,

Mac Dude

dchangeTest.mw

## DIM.................................

Asked by:

Hi:

how i can dimensionless a equation in maple?is there direct method for dimensionless equation in maple?for example i must dimensionless the below equation:

c1*f(x, t)+c2*(diff(phi(x, t), x))+c3*(diff(w(x, t), x, x))+c4*(diff(w(x, t), t, t)) = 0

dimensionless values are defined as:

X=x/l , T=(k/h)*t

where:

c1,c2,c3,c4 are constant cofficients.

my new equation must in terms of: X and T.

## A problem with dchange...

Asked by:

I have the following d.e.:

I need to change the s variable into a different one, where the new variable is defined by

(the old s shows up in the limit of the integral)

I tried dchange, but it chokes on this as I don't have an explicit representation of s in terms of Theta.

(I know the overall solution as other people smarter than me have solved this a long time ago, but I 'd like to have the derivation to understand it).

Mac Dude

## dchange pde maple...

Asked by:

Dear all,

I need your help

I have a problem with dchange ....  use the dchange command to transform pde to the
x[1], x[2].

> restart;
> with(PDEtools); with(LinearAlgebra);
> pde := diff(u(t), t, t)+2*GAMMA*(diff(u(t), t))+omega^2*u(t) = 0;
/ d  / d      \\           / d      \        2
|--- |--- u(t)|| + 2 GAMMA |--- u(t)| + omega  u(t) = 0
\ dt \ dt     //           \ dt     /
> deq1 := diff(u(t), t) = v(t);
d
--- u(t) = v(t)
dt
>
> deq2 := subs(deq1, pde);
/ d      \                       2
|--- v(t)| + 2 GAMMA v(t) + omega  u(t) = 0
\ dt     /
>
> dsolve({deq1, deq2}, {u(t), v(t)});
>
> eqns := [rhs(deq1) = lhs(deq1), rhs(deq2) = lhs(deq2)];
[        d            / d      \                       2     ]
[v(t) = --- u(t), 0 = |--- v(t)| + 2 GAMMA v(t) + omega  u(t)]
[        dt           \ dt     /                             ]
> y := [u, v]; b := diff(y(t), t);
[u, v]
[ d         d      ]
[--- u(t), --- v(t)]
[ dt        dt     ]
> A, b := GenerateMatrix(eqns, y(t));
Matrix(%id = 122038892), Vector[column](%id = 135944696)
# Return a vector of eigenvalue of A and matrix  whose columns are eigenvectors of A
> gnat := Eigenvectors(A);
> lambda := gnat[1]; Lambda := gnat[2];
Vector[column](%id = 135975976)
Matrix(%id = 136787860)
> Y := Vector([y]);
Vector[column](%id = 123771808)
> tr := solve(GenerateEquations(Lambda, [x[1], x[2]], Y), {u, v});
/           /                                    (1/2)
|      1    |                   /     2        2\
< u = ------ \-x[1] GAMMA - x[1] \GAMMA  - omega /      - x[2] GAMMA
|         2
\    omega

(1/2)\                 \
/     2        2\     |                 |
+ x[2] \GAMMA  - omega /     /, v = x[1] + x[2] >
|
/
>
> dchange(tr, pde, [x[1], x[2]]);

## convert(ode,...) and PDEtools[dchange] disagree......

Asked by:

I converted an ode using the built-in "convert" tool to check some calculations I had done by hand. To my surprise, there was an inconsistency. I converted the ode using PDEtools[dchange], reproducing the steps I had followed manually, and they checked out. So my question is: is there a sign error in convert? (and therefore a bug) or are both conversions correct, and if so are there any lessons to be learned? (is it related to the equation's symmetries?)

Thanks for your comments.

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