He is solving differential equations but with an analogue computer.

Doing it faster and with less doubts over fidelity and existence of a solution too.

Solving partial differential equations numerically and vetting the solution so obtained is not a trivial matters. Many things can go wrong in non obvious ways.

Analogue computers are a worthy alternative when applicable.

Calculus exists, but analytic solutions generally don't. Gaudi's chains and weights serve as an incredibly elegant mechanical computer that were only surpassed in the last few decades by CAD. Designers used mechanical splines until the advent of CAD in the 70's/80's.