Find values of a function for different parameters.

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?