Mathematica: How to resolve the issues in code for the system of PDEs?

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How to resolve the issues in code for the system of PDEs?
I hope you found a solution that worked for you :)
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Thanks to all those great people for their contributions!

(mathematica.stackexchange.com/users/57393/noor-aslam)Noor Aslam
(mathematica.stackexchange.com/users/58388/alex-trounev)Alex Trounev
(mathematica.stackexchange.com/users/58388/alex-trounev)Alex Trounev
A special thanks goes out to the (mathematica.stackexchange.com/questions/312480/how-to-resolve-the-issues-in-code-for-the-system-of-pdes)Stackexchange community

I wish you all a wonderful day! Stay safe :)
If anything is off, please write me at peter D.O.T schneider A.T ois42.de

matrix linear-algebra code-review




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