Continuous System Simulation

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.- Semiâ€"analytic Algorithms.- Spectral Algorithms.- Singleâ€"step Integration Methods.- Introduction.- Rungeâ€"Kutta Algorithms.- Stability Domains of RK Algorithms.- Stiff Systems.- Extrapolation Techniques.- Marginally Stable Systems.- Backinterpolation Methods.- Accuracy Considerations.- Stepâ€"size and Order Control.- Multiâ€"step Integration Methods.- Introduction.- Newtonâ€"Gregory Polynomials.- Numerical Integration Through Polynomial Extrapolation.- Explicit Adamsâ€"Bashforth Formulae.- Implicit Adamsâ€"Moulton Formulae.- Adamsâ€"Bashforthâ€"Moulton Predictorâ€"Corrector Formulae.- Backward Difference Formulae.- NystrÃœm and Milne Algorithms.- In Search for Stifflyâ€"stable Methods.- Highâ€"order Backward Difference Formulae.- Newton Iteration.- Stepâ€"size and Order Control.- The Startup Problem.- The Readout Problem.- Second Derivative Systems.- Introduction.- Conversion of Secondâ€"derivative Models to Stateâ€"space Form.- Velocityâ€"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.- Gridâ€"width Control.- PDEs in Multiple Space Dimensions.- Elliptic PDEs and Invariant Embedding.- Finite Element Approximations.- Differential Algebraic Equations.- 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.- Singleâ€"step Formulae.- DASSL.- Inline Integration.- Inlining Implicit Rungeâ€"Kutta Algorithms.- Stiffly Stable Stepâ€"size Control of Radau IIA.- Stiffly Stable Stepâ€"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 Sampledâ€"data Systems.- State Events (1. Multiple Zero Crossings, 2. Single Zero Crossings, Singleâ€"step Algorithms, 3. Single Zero Crossings, Multi-step Algorithms, 4. Nonâ€"essential State Events).- Consistent Initial Conditions.- Objectâ€"oriented Descriptions of Discontinuities (1. The Computational Causality of ifâ€"Statements, 2. Multiâ€"valued Functions).- The Switch Equation.- Ideal Diodes and Parameterized Curve Descriptions.- Variable Structure Models.- Mixedâ€"mode Integration.- State Transition Diagrams.- Petri Nets.- Realâ€"time Simulation.- Introduction.- The Race Against Time.- Suitable Numerical Integration Methods.- Linearly Implicit Methods.- Multiâ€"rate Integration.- Inline Integration.- Mixedâ€"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 Systems Simulation.- Quantized State Systems.- Quantization-based Integration.- Introduction.- Convergence, Accuracy, and Stability in QSS.- Choosing Quantum and Hysteresis Width.- Input Signals in the QSS Method.- Startup and Output Interpolation.- Second-order QSS.- Algebraic Loops in QSS Methods.- DAE Simulation with QSS Methods.- Discontinuity Handling.- Real-time Simulation.- Open Problems in Quantizationâ€"based Methods.