Find values of a function for different parameters.

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I have Z as a function of posisition and time:
Z = Z(x,y,t)
There are some fixed parameters say:
a,b,c
I am interested in functional values of Z for varying a, b and c at different positions and time. I want variation of Z in x, y and t for different a, b and c. I want to do it programmatically. What is the optimal way to do this?

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