Continuous System Simulation describes systematically and methodically how mathematical models of dynamic systems, usually described by sets of either ordinary or partial differential equations possibly coupled with algebraic equations, can be simulated on a digital computer.

This reference describes in detail how to build mathematical simulations of systems that change continuously over time. The topics covered include numerical integration, simulation of stiff systems, simulation of marginally stable systems, simulation of noisy systems, model validation techniques, simulation verification, dynamic nonlinear programming, simulation hardware and software. This highly computer-oriented text introduces numerical methods and algorithms alongside applications and conceptual tools. Homework problems, suggestions for research projects, and open-ended questions conclude each chapter.

Introduction, Scope, Definitions.- Modeling and Simulation: A Circuit Example.- Modeling vs. Simulation.- Time and Again.- Simulation as a Problem Solving Tool.- Simulation Software: Today and Tomorrow.- Basic Principles of Numerical Integration.- Introduction.- The Approximation Accuracy.- Euler Integration.- The Domain of Numerical Stability.- The Newton Iteration.- Semi-analytic Algorithms.- Spectral Algorithms.- Single-step Integration Methods.- Introduction.- Runge-Kutta Algorithms.- Stability Domains of RK Algorithms.- Stiff Systems.- Extrapolation Techniques.- Marginally Stable Systems.- Backinterpolation Methods.- Accuracy Considerations.- Step-size and Order Control.- Multi-step Integration Methods.- Introduction.- Newton-Gregory Polynomials.- Numerical Integration Through Polynomial Extrapolation.- Explicit Adams-Bashforth Formulae.- Implicit Adams-Moulton Formulae.- Adams-Bashforth-Moulton Predictor-Corrector Formulae.- Backward Difference Formulae.- Nyström and Milne Algorithms.- In Search for Stiffly-stable Methods.- High-order Backward Difference Formulae.- Newton Iteration.- Step-size and Order Control.- The Startup Problem.- The Readout Problem.- Second Derivative Systems.- Introduction.- Conversion of Second-derivative Models to State-space Form.- Velocity-free Models.- Linear Velocity Models.- Nonlinear Velocity Models.- Stability and Damping of Godunov Scheme.- Explicit and Implicit Godunov Algorithms of Different Orders.- The Newmark Algorithm.- Partial Differential Equations.- Introduction.- The Method of Lines.- Parabolic PDEs.- Hyperbolic PDEs.- Shock Waves.- Upwind Discretization.- Grid-width Control.- PDEs in Multiple Space Dimensions.- Elliptic PDEs and Invariant Embedding.- Finite Element Approximations.-Differential AlgebraicEquations.- Introduction.- Causalization of Equations.- Algebraic Loops.- The Tearing Algorithm.- The Relaxation Algorithm.- Structural Singularities.- Structural Singularity Elimination.- The Solvability Issue.- Differential Algebraic Equation Solvers.- Introduction.- Multi-step Formulae.- Single-step Formulae.- DASSL.- Inline Integration.- Inlining Implicit Runge-Kutta Algorithms.- Stiffly Stable Step-size Control of Radau IIA.- Stiffly Stable Step-size Control of Lobatto IIIC.- Inlining Partial Differential Equations.- Overdetermined DAEs.- Electronic Circuit Simulators.- Multibody System Dynamics Simulators.- Chemical Process Dynamics Simulators.- Simulation of Discontinuous Systems.- Introduction.- Basic Difficulties.- Time Events.- Simulation of Sampled-data Systems.- State Events (1. Multiple Zero Crossings, 2. Single Zero Crossings, Single-step Algorithms, 3. Single Zero Crossings, Multi-step Algorithms, 4. Non-essential State Events).- Consistent Initial Conditions.- Object-oriented Descriptions of Discontinuities ( 1. The Computational Causality of if-Statements, 2. Multi-valued Functions).- The Switch Equation.- Ideal Diodes and Parameterized Curve Descriptions.- Variable Structure Models.- Mixed-mode Integration.- State Transition Diagrams.- Petri Nets.- Real-time Simulation.- Introduction.- The Race Against Time.- Suitable Numerical Integration Methods.- Linearly Implicit Methods.- Multi-rate Integration.- Inline Integration.- Mixed-mode Integration.- Discontinuous Systems.- Simulation Architecture.- Overruns.- Discrete Event Simulation.- Introduction.- Space Discretization: A Simple Example.- Discrete Event Systems and DEVS.- Coupled DEVS Models.- Simulation of DEVS Models.- DEVS and Continuous SystemsSimulation.- Quantized State Systems.- Quantization-based Integration.- Introduction.