Although many programs have built-in various methods for finding the steady state nowadays, their actual implementations are often quite unsatisfactory regarding algorithm efficiency and reliability. We improved and checked procedures built on both e-algorithm and sensitivity analysis in time domain. First of all, it was clearly demonstrated that increasing demands on the overall numerical accuracy do not lead to an excessive number of necessary integration steps and therefore LU factorizations correspondingly. This feature is especially significant for the suggested procedure based on the e-algorithm. Furthermore, the practical experiments confirmed that a proposed arrangement of the extrapolation method is greatly insensitive to its order, which is even more important because a program user is unable to estimate the appropriate order for complicated circuits well. The properties of the methods are demonstrated using rectifier, C-class amplifier, and LNA for which exceptional attention was given to checking the insensitivity of the extrapolation to its order.