I am trying to implement a calculation based on the demonstration “Transient Cooling of a Sphere.” The Mathematica function NDSolveValue is used to solve a partial differential equation subject to one initial condition and two boundary conditions. One of the boundary conditions is that the solution must be finite at r=0. Symbolically, it is expressed as u{0,t]<Infinity. But if I use this form of the boundary condition in the NDSolveValue function, I get an error message that an equation or list of equations is expected. So what is the correct syntax for imposing this boundary condition within the NDSolveValue function?
Please give more details and include any code you have already tried.
Here is a link to the Wolfram demo where some details are furnished:
https://demonstrations.wolfram.com/TransientCoolingOfASphere/
I have also added a notebook file and associated files to the post. If anything is unclear, please ask for clarification.
numbers.txt (184 Bytes)
turkey2020temp.nb (15.4 KB)
warming.txt (1.77 KB)
One of the 3 files I uploaded was not the file needed by the notebook. I have now edited the previous post to include the needed file.
Should I interpret the lack of replies to mean that the NDSolveValue function cannot handle a finite value boundary condition of the type described?
asmar, pde, p. 255 - as to the meaning of “y(0) is finite” used in that book, used in a proof of a theorem
if a condition is y(0) is finite, assuming some c1 is upon a term that is not finite (series), set c1 equal to zero on that term.
(the situation presented was some y = c1 y1 + c2 y2, y2 was a non-finite series and “deleted”, meaning the condition was mean to read: y = y1 only in this case of this theorem)
that was in a theorem involving bessel J so it is not impossible it would be the same issue. issues of catalogued series solutions are … delicate (how many solutions of what kind whether ln should be seen). it would be best to check your solution regardless.