Dear all, 

I am new to Maple, bit I am getting familiar with it. My current interest is in Lie Symmetry analysis of systems of PDE's such as mass, momentum, and energy balance equations in fluid dynamics, for example.

I have carried out a Lie Symmetry analysis for a single PDE's -- attached herewith. I know it to be correct because it is already published. What I want to do now is how to write down more than 1 PDE's and carry out a similar Lie Symmetry analysis to this system of PDE's. I have been unable to find an example on the web.

Can you advise please - especially how to enter a systems of PDE's as apposed to just one PDE.

Thanks

Nadeem Malik

Sheet9.mw

Dear Maple users,

I want to find an expression for the Fourier Transform (FT) of an expression like  f(t)=exp(-t^2)/t^a, where a>0 is a constant.

I note that integer values of a (postive or negative) is ok; but non-integer fails. See sheet attached where I have tried 1 or 2 cases, a=0, 1, 0.3, etc.

So the questions are:

(1) how can I find the FT of the above for typical non-integer values of a>0 ?

(2) how can I find the FT of the above for general a -- i.e. declare a as a parameter?

Thanks

Nadeem

Download Sheet_fourier_1.mw

Dear Maple users,

I am progressing, but one last hitch, see below. A want the invariants of the PDE below. However, the final expression is too general to be useful. I would like to insert specific values for F1(R), F2(R), F3(R), and F4(R):

F3=F4=0; and F2=1, and F3(R)=aR, where a is a constant. R is one of my independent variables (the Reynolds number). 

I would like to do this at the step where the Infinitiesimals are generated by

For example, the first entry would then be, infinies:=[ _xi[y](y, R, l, u) = y, ... ]. Then Invariants should give me much simplified expressions which I need.  How can i do this?

Thanks

Nadeem

Hello,

Real beginner, never used Maplw before. I want to analyse PDE's through Lie symmetry analysis -- get the infiniteeimals and then generate the invariants. I am going through the standard examples on the help within Maple, but I am stuck on a basic issue which prompts me to think that there may be something different in my version of Maple (although I downloaded it from TTU which I presume should be the latest version).

Here's what I get >>>>>

Loading PDEtools

with(PDEtools, InfinitesimalGenerator, declare);
               [InfinitesimalGenerator, declare]

declare(u(x, t));
               u(x, t) will now be displayed as u
U: diff_table(u(x, t)):
PDE := U_x,x - U_t = 0;
                    PDE := U_x,x - U_t = 0
show;
                       U_x,x - U_t = 0
Infinitesimals(PDE)
Error, (in PDEtools:-Infinitesimals) missing dependent variables

>>>>>

I have also tried:

Infinitesimals(PDE, u)
Error, (in PDEtools:-Infinitesimals) not a PDE system w.r.t u

and:

Infinitesimals(PDE, U)
Error, (in PDEtools:-Infinitesimals) not a PDE system w.r.t U
 

There are many other issues, but let's deal with this one first.

Thanks

Best wishes

Nadeem