@nm 

Hi, I appreciate your looking into a potential numerical solution. I understand the limitations.

In the meantime, I will make sure that all the four BCs are consistent with the IC and vice versa. Perhaps a closed form solution is still possible for a better posed problem that still reflects reality.

Best Regards,

Joseph Thodiyil

@nm Hi, even after correcting the inconsistency between BC2 and the IC as described, Maple did not produce a solution. No errors were recorded either.

Is there a numerical solution option for PDEs just as there is one for ODEs? I shall check with ?pdsolve in Maple.

Thanks,

Joseph Thodiyil

@nm Hi, I appreciate the insight that you have provided in solving this problem.

Yes, you are correct on both counts:

h(r,z,t) := 0

In addition, the IC and 2nd BC are inconsistent.

BC2: -alpha*u'_z| _{z = 0} = 0

Corrected IC: u(r,z,0) = Psi_i

Where Psi_i is a known fixed value.

With this change, I shall make another attempt this afternoon to see if there is a closed-form solution.

Thank you once again.

Best Regards,

Joseph Thodiyil

@tomleslie Hi, I do greatly appreciate your painstakingly going through the Articolo code and showing that it does work. I am very new to Maple and it will take me a little while longer to get to understand all the nuances associated with using the software.

Mapleprimes - what a great community and contributors! I am thankful.

Best Regards,

Joseph Thodiyil

@nm Hi, once again I do appreciate your insight and help with resolving this problem completely.

Mapleprimes - what a community with great contributors!

Best Regards,

Joseph Thodiyil

@nm Hi, it has all worked out well with this problem, have even plotted it for various values of time, t. Thanks to you!

Now I would like to evaluate u'_x | _{x = 1} for any given value of time, say t = 10.

Could I do something like this:

v(x,t):=diff(u(x,t),x): evalf(v(1,10);

Thanks,

Joseph Thodiyil

@dharr 

I appreciate your guidance on this. Nice plots, just like in the textbook.

I am still learning Maple, getting ready for a Numerical Methods class in the Summer of 2021.

Best Regards,

Joseph Thodiyil

@nm 

Thank you very much for your time and effort.

The solution now comes out good, but when I try to plot the solution, I get some error messages.

The updated worksheet is attached. Please take a look and let me know where I have gone wrong.

PDE_Sol_Plot.mw

Thanks again.

Best Regards,

Joseph Thodiyil

@mmcdara 

Thanks very much!

@mmcdara 

I am just one week into Maple.

I appreciate your quick response and for the elegant solution. This is just an excellent community and I appreciate your time and enthusiasm.

Best Regards,

Joseph Thodiyil