Suggest a suitable technique for mathematical modeling of DC Electric arc

I am working on a physics topic, "mathematical modeling of 48V DC Electric Arc". I have collected various parameters which influence arc phenomena, which are in the form of differential equations. Now I want to place all the parameters into a single system to define the characteristics of arc. After modeling, I should be able to use this model in such a way that, I can change the input parameters to observe changes in the output parameters of the arc. Please suggest me a suitable technique to model this in Matlab/Simulink. Thankyou in advance.