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How can I compute and graph a recursive 3D parametric equation after each iteration?

Basically, I have a function defined by $A(x,y,t+1)=A(x-1,y,t)+A(x,y-1,t)+A(x+1,y,t)+A(x,y+1,t)-A(x,y,t)$, with initial condition $A(x,y,0) = \cos(i)^2, x = \cos(i), y = \sin(i)$. I can graph the ...
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How to solve a ParametricNDSolve issue when the system seems to be stiff?

I have a problem with ParametricNDSolve[]. Mathematica gives the warning that a stiff system is suspected. I have varied the methods but unfortunately I was not ...
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Parameter sensitivities of ParametricNDSolveValue involving numerical function

This is a followup of my former question from here. Consider the code ...