1. A system for analyzing a model of an electronic circuit comprising at least one non-linear circuit element, the system comprising: a computer, the computer configured to: replace the at least one non-linear circuit element with a linearized circuit model that approximates a behavior of the at least one non-linear circuit element; insert into an element matrix a calculated value corresponding to the linearized circuit model for a time step; and perform a numerical operation on the element matrix to effectively invert the element matrix.