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.- 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.- Nystrom 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 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.- 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 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 Quantization--based Methods.