HYBRID METHODS OF HIGH ACCURACY ORDER FOR NUMERICAL ANALYSIS IN THE TIME DOMAIN OF STIFF AND OSCILLATING CIRCUITS

This paper considers the problems of numerical analysis of electronic circuits in the time domain that arise when using modern circuit simulators based on SPICE. Time-domain analysis of circuits through modern electronic simulators is realized by means of Gear’s methods and the trapezoidal method. An important property of models of real electronic circuits and especially of RF circuits is simultaneous stiffness and oscillability of these models. In turn, Gear’s methods can lose stability for oscillating circuits’ analysis, because these methods are not P-stable, and the trapezoidal method has a sufficiently high error for stiff circuits’ analysis, because it is not L-stable. The aim of this paper is to develop hybrid Land P-stable methods based on the combination of various numerical methods for solving ordinary differential equations which provide a high accuracy of numerical simulation in the time domain of stiff and oscillating circuits. Hybrid methods are built on the basis of the known Rado IIA and Lobatto IIIA methods, which are subclasses of implicit Runge-Kutta methods. Comparative analysis of the known methods and the proposed hybrid methods demonstrates high accuracy of the latter methods for time-domain simulation of stiff and oscillating circuits and systems. Hybrid methods are also effective for numerical solving differential-algebraic equations that describe arbitrary electrical circuits.

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