Wow, that does not make any sense. Not sure how that happened.

So what I did was go from

V(x,t) -> V(x/l(t),t) 

So I transformed the x coordinate by dividing by l(t) (which is how my beam lngth is changing with time). This gives me a new coordinate system which makes my boundary condition more simple making the PDE possible to solve.

So now my numeric solution is in the form V(x/l(t),t) and I'm trying to take it back to V(x,t). So i have to multiply through by l(t).

In case you were wondering..l(t) = 1 - a*cos(wt)

@tomleslie 

In the temp variable I wasn't able to access the 2x2 matrix of points. I can do temp[2,1], etc, but the matrix is in temp[3,1] but for some reason this doesn't work. I was able to manually "view" the variable and matrix and then hit export.rmation was x/l(t). So now I'm trying to multiply the output by the l(t) to put it back in the original coordinate system. This is the part I'm having a hard time doing. I tried to use the function to evaluate it at certain points but then I have to multiply the whole x coordinate by the l(t).

This is the output graph in matlab once the data is transformed.

This is the matlab code I used to transform it back

w_bearing = 9.86;
filename = ['SS_mapleOutput_w_' num2str(w_bearing, '%.2f.xlsx')];
A = xlsread(filename);
%Convert to familiar format
amp = A';
time = linspace(0,5,length(A))';
xax_original = linspace(0,1,length(A));
a = 0.05;

for ii = 1:length(time);

lt = 1-a*cos(w_bearing*time(ii));
xax_label = xax_original.*lt';
plot(xax_label,amp(ii,:)); %Plot at time(ii)
axis([0 1+a -.5 0.5])

...... Formatting stuff ....

end

Download ODE45_Comparison.mw

I will look into those a bit more. A single-software solution would be the ideal.

I was able to find a crude but easy way to move the data over from maple to matlab. Using the getdata command it will extract the matrix. You can go through the variable and export the data to an excel file then import it to matlab. Didn't take very long at all.

@tomleslie 

Thanks for the thourough reply. 

There is a maple PDE toolbox but I do not have it so that is why I resorted to going to maple. School licensing and such. I may try do mess around with the data in maple a bit more, maybe I am able to get the desired result in the format I want.

@tomleslie 

Ah, I understand now. The little things makes all the difference. Thanks.

I see there are also ways to find solutions in series form? Do you think something like this is possible? I took a stab at it and it doesn't look like it. Or a traveling wave solution? I see that it says the solution is not separable when i test for separability?

I'm just trying to explore other types of things I read about. This is all new so i'm seeing what all is available.

@Preben Alsholm 

Yes, I remember reading that on the site where the equation needs to be in diff format and the boundary/time conditions needs to be in D format (since D can be evaluated at a point). I was under the impression when I type equations as "pde:=diff(u(x,t),t)=diff(u(x,t),x,x);" that this was the diff format. The examples also write the equations in this format and don't convert for solving.t

This is a help page (below) for Numerical Solutoins to PDE Boundary Value Problems and I'm not seeing a conversion to D format so I think that is why I'm a bit confused that the help page solves problems without converting.

http://www.maplesoft.com/applications/view.aspx?SID=4259&view=html

@Preben Alsholm 

Ah, yes!! Thank you so much.

I made a similar mistake in matlab one time using i as a variable in a loop and then it re-defined the imagery value i and it made all my results look wrong.

Quick question though...

1. Why do I need to do this?

convert(PDE1, diff);
## to
PDE1 := convert(PDE1, diff);

I ininitially converted it so that it would be in a more familiar format and it was more for just a visual inspection. It sounds like this is necessary for solving though?

2. With the numeric approach does it try convert it to an ODE? Is it possible to see this ODE? In the paper I'm trying to follow it studied the equation and looked at regions of instability. It used the ODE it converted from the PDE though to do this.

Thanks again!

@Preben Alsholm 

This is the error I get whjen trying the numeric approach. Here is the file I'm looking at.

Thesis_Pde2_attempt.mw

Error, (in pdsolve/numeric/process_PDEs) number of dependent variables and number of PDE must be the same

Thanks, I will use this from now on, it seems to be the better appraoch.

@Preben Alsholm 

1. I edited the subscripts and just used E and I. This did not fix it.

2. I spent a significant amount of time trying to get maple to correctly recognize my functions and to take the derivatives correctly. The superflous parantheses caused it to work correctly (this makes me feel like maple is very fickle and a bit of a nuissance to use). This is probably because of my inexperience, but it seems to actually recognize it correctly.

3. This is a PDE from a research paper. It may not have an analytical solution. In the paper he used an approximation teqnique (The Galerkin method) but I was hoping to see some type of general solution to get some insight into the behavior.

Do you see 5 boundary conditions in my maple code?? There should be 4 as in the research article.

4.Numeric may give some insight, but why would extra boundary conditions be needed for a numeric solution? In this case I'm not sure how I would addd another.

Thanks again for the help :)

@tomleslie 

Okay, I was able to define the function. It seems that it still cannot be solved though? Am I making other small mistakes? Is there another route to go to solve? Any thoughts?

Here is my updated code.

Thesis_Pde2_attempt.mw

@tomleslie 

1. I had no idea that I had a choice in using 2D math vs. 1D. I come from a matlab background and this 2d math input has been quite frustrating so that is good to know.

2. My variable i'm solving for is V(xi, vartheta). 

3. phi() is a defined function: phi = 1-a*cos(2*vartheta);

I didn't put this function in because I was trying to compare my formulation with the paper to see if the equation is correctly transformed.

Thanks for the input!

NeverMind, figured it out! Craziness it's always the little things...

@GeorgeReynolds 

Ah yes, didn't realize that was an option.

PDE_change.mw

Thesis_PDE.mw

Thanks