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Should I use with the case of using or in case of using in the following paragraph?

We have demonstrated its identification ability and compared its performance with the case of using central finite differences from Matlab for the gradient calculation.

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in case of is a set phrase that's used to describe what to do if some particular event occurs:

In case of fire, leave via the closest exit.

This is not applicable to your sentence. In your case, with is not part of the phrase with the case of using, it's the preposition that goes with compared, to indicate what is being compared to the the earlier item. It's part of the general pattern

We compared X with Y.

You could also replace with with to.

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