Numerical simulation and modelling are witnessing a resurgence. Designing systems with integrated wireless components, mixed-signal blocks and nanoscale, multi-GHz “digital” circuits is requiring extensive low-level modelling and simulation. Analysis and design in nonelectronic domains, notably in systems biology, are also relying increasingly on numerical computation.
Sections 2–8 of this Monograph provide an introduction to the fundamentals of numerical simulation, and to the basics of modelling electronic circuits and biochemical reactions. The focus is on a minimal set of concepts that will enable the reader to further explore the field independently. Differential–algebraic equation models of electronic circuits and biochemical reactions, together with basic numerical techniques — quiescent, transient and linear frequency domain analyses, as well as sensitivity and noise analyses — for solving these differential equations are developed. Downloadable MATLAB implementations are provided.
The last two chapters provide an introduction to computational methods for nonlinear periodic steady states and multi-time partial differential equation (PDE) formulations, followed by an overview of model order reduction (MOR) and, at the end, a glimpse of some applications of oscillator MOR — in circuits (PLLs), biochemical reaction–diffusion systems and nanoelectronics.
