State variable changes to avoid non computational issues

This paper is about the numerical simulation of nonlinear analog circuits with ”switch” components, such as diodes. A ”switch” component is an electrical device that may or may not conduct, depending on the state of the circuit. The problem with ”switch” components is that the topology of the circuit is variable and so, apparently, it is not possible to describe the system with a single differential equation and solve it using standard numerical methods. This paper shows how to choose an appropriate state variable and overcome the above difficulties.