Scattering-based numerical methods are increasingly applied to the numerical simulation of distributed time-dependent physical systems. These methods, which possess excellent stability and stability verification properties, have appeared in various guises as the transmission line matrix (TLM) method, multidimensional wave digital (MDWD) filtering and digital waveguide (DWN) methods. This text provides a unified framework for all of these techniques and addresses the question of how they are related to more standard numerical simulation techniques.Covering circuit/scattering models in electromagnetics, transmission line modelling, elastic dynamics, as well as time-varying and nonlinear systems, this book highlights the general applicability of this technique across a variety of disciplines, as well as the inter-relationships between simulation techniques and digital filter design. * provides a comprehensive overview of scattering-based numerical integration methods. * reviews the basics of classical electrical network theory, wave digital filters, and digital waveguide networks. * discusses applications for time-varying and nonlinear systems. * includes an extensive bibliography containing over 250 references. Mixing theory and application with numerical simulation results, this book will be suitable for both experts and readers with a limited background in signal processing and numerical techniques.