Abstract <p>An analysis of numerical-analytical methods for transient analysis in linear electrical circuits was carried out and a methodology for their combination with the circuit determinants method was proposed. Based on this approach, two variants of the algorithm for transient analysis in linear electrical circuits were developed, namely, the first is based on dividing the solution into free and forced components of oscillations, and the second is based on representation in the form of transient and steady-state components of oscillations. An example of calculating a linear electrical circuit is given, and the advantages and disadvantages of the proposed approaches are shown.</p>