I am new to using the Odesolve and Pdesolve functions; see attached Mathcad 15 file.
Thanks much for any help,
Hi Reg Curry,
The partial derivatives of the unknown functions are not written correctly.
with their related initial and boundary conditions ....
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.
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?
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.
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
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.
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.