A great deal of mathematical calculation is done by many researchers regarding switched-mode power conversion. Only a very little of it is useful to the designer. Much of it is far too complicated to use, and much of it does not answer the questions that a working engineer asks.
We will stick to math that is useful in designing the Boostbuck topologies, is linear except in the case of DC conditions, and is design oriented.
The various forms of SPICE are NOT useful for design. The SPICEs are simulation programs, not design programs. That is, they can only be used after a circuit is designed, to confirm performance. They are far too cumbersome to be used iteratively in actual design.
Their most appropriate application is design verification after the fact. Often, this function is driven by the corporate legal department, which is worried about a design not meeting its advertised spec, and the danger of lawsuits. Even here, the simulation of a finished design is so elaborate as to be impracticable, engaging inordinate amounts of expensive computer time….
Note that what I am saying is really that the computer is useless for design purposes in the field of Power Electronics. Pencil and paper calculations using the Canonical Model and design oriented equations are both necessary and sufficient. In the end, these complement the engineer’s refined judgement, and are entirely adequate.
I might say that I speak from personal experience at the MIL, Industrial, and Commercial levels. I have been entirely successful in completing designs using such methods, and have yet to employ a computer for anything but schematic capture, BOMs, E-mail, and so on.
Meanwhile, I have watched computer aided designs languish, and have often been the one called on to rescue them from failure! In all, I have earned > 1/3 x 1M$ in pay, and have no OOPSes in the field.