C.29.2:11.5 - Keep structural reformulation and numerical solution distinct

ModelingToolkit’s model-building reference, “System simplification” and “Exploring the results of simplification”, describes reformulating equations and recovering eliminated variables through stored expressions. Adopt that pairing in :4.2 and :5.4. Hand substitution suffices for the small circuit; a symbolic compiler becomes useful when model size or changing equations make that work substantial.

Its initialization tutorial distinguishes required conditions from guesses and shows how changing the givens can require releasing a retained constraint. Adapt that distinction when parameters or initial quantities become unknowns. Consistency of an initial system and numerical success in finding its solution are different questions.

Dyad’s transient-analysis documentation separates the initial-value problem from algorithm and tolerance choices. Adopt that separation: structural reduction supplies a computational problem and recoverable outputs; numerical analysis supplies an appropriate solution method and accuracy argument. Reopen the affected choice when equations, initial constraints, requested outputs or accuracy change.