Help! Odesolve and Pdesolve questions

[regcurry]

I am new to using the Odesolve and Pdesolve functions; see attached Mathcad 15 file.

1. Okay, I figured out that the independent variable of Odesolver must be x and cannot be another variable like t.
2. I also discovered that the x range cannot be defined as a 2 row 1 column vector even though the Mathcad 11 manual indicates that is possible.  This must have changed.  However, it is possible in the Pdesolver.
3. Okay, I discovered that the independent variable must be an integer in integer steps, so I cannot define times less than 1.
4. As shown in the attached Mathcad 15 file, I can solve a simpler form of the transmission line equations for a buried line where V is assumed constant over the line with the Odesolver.  I am able to include  time (i.e. x) varying resistance and inductance of the buried line with a time varying driver E(x).
   
   
5. In the solution to this ODE as shown in the attached, how do I determine the actual values of x (i.e., the actual time values).
6. Now, when I try to solve the complete buried transmission line equations with the Pdesolver, I get the error that V is undefined as shown in the attached.  Why?
   
   with R(t) and L(t) the same as in the above example, and Gg(t), and Cg(t) similarly defined
7. And, as in 5 above, how do I determine the actual values of t if I ever get this solved?

Thanks much for any help,

Reg Curry

[-MFra-]

Hi Reg Curry,

The partial derivatives of the unknown functions are not written correctly.

with their related initial and boundary conditions ....

[Werner_E]

You also have to use literal indices (V.x) and not vector indices (V[x) as you did. Probably that was the reason you ended up with the multiplications FM pointed you to.

Furthermore you have too many initial conditions - you will have to delete E(0)=0 as you don't solve for E anyway.

After correcting all of the above it works, but after a while we get the error "Repeated singularity problems encountered". Maybe you'll have to recheck your equations and conditions.

[regcurry]

Thanks much guys.  Both F.M. and Werner are correct.  Not only do I have only 3 neurons left working, my eyesight is failing at 74.  I accidentally first used vector indices and then just deleted them and inserted literal indices. Apparently that caused the multiplication problem.  I never noticed it.

F.M--the equations I am trying to solve have a uniform electric field over the entire line, that is the reason for the syntax of the equations.

Werner--after making the corrections you and F.M. noted, I get the same singularity problem you note.  At present, I am not sure where the singularity problems arise.  I have solved the same equations using explicit differencing in Mathcad with no problem.  I need to do some more thinking on this.

Thanks again guys.  Is there a way to give both of you the credit for the correct answer to my original question?

[-MFra-]

Thanks for the clarity about the uniform electric field along the line, I thought it was excited at one extreme. Even for me, the program does not work. Let's see if Werner succeeds.

I would still wait to see if there are others, in the community, who want to contribute, with their help and experience, in dealing with the problem.

Greetings

[regcurry]

The solve block apparently does not like the values of Gg(t).  If I fix that at 5x10^-2, it works unless I choose a ground conductivity greater that 10^-3.  So, I clearly don't understand the solution space for these two PDEs.  Perhaps I need to stick with explicit finite difference.  To solve this problem with that method takes over 30 minutes, but it does work.  I have attached a pdf of that Mathcad sheet after evaluation is complete.

If Ground conductivity = 10^-2

[Werner_E]

I wasn't able to make it working, too.

I played around with different (silly) functions for E(t) and it worked.

So maybe we run into numerical inaccuracies or the like. Not sure, though.

For whatever it may be worth I attach a screenshot of one of the tries. With this one I also had to lower the value of xpoints to avoid the error.

BTW, I am surprised that you plot I(Tmax,t), after all, Tmax is a t-value, not an x-value.

[regcurry]

‌The I(Tmax,t) was a mistake.  I intended to write I(Lz,t).  I told you I am 74 with only 3 neurons left and poor eyesight.  LOL

Nevertheless, thanks again to you and F.M.  You answered my basic question on my incorrect syntax for pdesolve.  I was just hoping for a faster method than explicit finite differencing.

Take care,

Reg