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.- 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.-

From the reviews: "This is a graduate-level textbook, a sequel to continuous system modeling ... . The text provides a plentiful number of exercises and projects at various levels of difficulty. Each chapter has a carefully selected list of references." (William J. Satzer jun, Zentralblatt MATH, Vol. 1112 (8), 2007)