Continuous System Simulation

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.

Includes homework problems, suggestions for research projects, and open-ended questions at the end of each chapter Includes supplementary material: sn.pub/extras

Inhalt
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.- Semianalytic Algorithms.- Spectral Algorithms.- Singlestep Integration Methods.- Introduction.- RungeKutta Algorithms.- Stability Domains of RK Algorithms.- Stiff Systems.- Extrapolation Techniques.- Marginally Stable Systems.- Backinterpolation Methods.- Accuracy Considerations.- Stepsize and Order Control.- Multistep Integration Methods.- Introduction.- NewtonGregory Polynomials.- Numerical Integration Through Polynomial Extrapolation.- Explicit AdamsBashforth Formulae.- Implicit AdamsMoulton Formulae.- AdamsBashforthMoulton PredictorCorrector Formulae.- Backward Difference Formulae.- Nyström and Milne Algorithms.- In Search for Stifflystable Methods.- Highorder Backward Difference Formulae.- Newton Iteration.- Stepsize and Order Control.- The Startup Problem.- The Readout Problem.- Second Derivative Systems.- Introduction.- Conversion of Secondderivative Models to Statespace Form.- Velocityfree 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.- Gridwidth 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.- Singlestep Formulae.- DASSL.- Inline Integration.- Inlining Implicit RungeKutta Algorithms.- Stiffly Stable Stepsize Control of Radau IIA.- Stiffly Stable Stepsize 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 Sampleddata Systems.- State Events (1. Multiple Zero Crossings, 2. Single Zero Crossings, Singlestep Algorithms, 3. Single Zero Crossings, Multi-step Algorithms, 4. Nonessential State Events).- Consistent Initial Conditions.- Objectoriented Descriptions of Discontinuities ( 1. The Computational Causality of ifStatements, 2. Multivalued Functions).- The Switch Equation.- Ideal Diodes and Parameterized Curve Descriptions.- Variable Structure Models.- Mixedmode Integration.- State Transition Diagrams.- Petri Nets.- Realtime Simulation.- Introduction.- The Race Against Time.- Suitable Numerical Integration Methods.- Linearly Implicit Methods.- Multirate Integration.- Inline Integration.- Mixedmode 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.-