ABSTRACT
This chapter explores the numerical properties of relaxation-based integration methods. Considerable progress has been achieved to relaxation-based methods, also called third-generation simulation methods. The chapter discusses the concept of relaxation methods that arises from the iterative methods of linear algebraic equations solution. The main idea used in relaxation methods is decoupling of circuit equations. The differences between relaxation methods begin with the level at which decoupling takes place. Decoupling of Ordinary Algebraic Differential Equations before discretization, and discretization applied to each decoupled component separately lead to waveform-re-laxation (WR) analysis. A slight improvement of WRA introduced by R. A. Saleh and J. K. White is known as waveform-relaxation Newton analysis (WRNA). It is based on the concept of waveform Newton (WN) iterations which can be used for time-domain analysis instead of the one-point Newton-Raphson iterations. The concept of WN iterations can be explained using the previously introduced nodal description with initial conditions.
