Modelling for Mathematics & IT

Good day! It is necessary to solve a system of 12 differential equations with an abundance of logical "if" conditions. I solve in Wolfram Mathematica, but the standard NDSolve methods do not work because of these conditions, I implement the Runge-Kutta method manually, but I get unsatisfactory results and a very long solution. I will be glad to cooperate with a mathematician who can help solve my problem.

It is necessary, within the framework of working with programmers and data scientists, to develop a model for monitoring the technical condition and process parameters in the fractionator.

I have about 12 articles in high-ranking scientific journals, wide experience in working with data. Good knowledge of differential calculus.