This book introduces a practical approach to the modelling and computation of real-world systems. Multibody dynamics, planar and spatial modelling, and numerical methods are all pursued to obtain information about the behaviour of various dynamical systems. Each study presents the method of modelling and the ensuing differential equations governing the system behaviour. Integration of the equations yields results which are carefully discussed and which indicate how useful information may be obtained from the study. The studies include planar mechanisms, heavy equipment, automobile crash simulation and a spatial planetary system example. Research students, scientists and engineers will appreciate the practical approach taken in this book.

This book introduces a practical approach to the modelling and computation of real-world systems. Multibody dynamics, planar and spatial modelling, and numerical methods are all pursued to obtain information about the behaviour of various dynamical systems. Each study presents the method of modelling and the ensuing differential equations governing the system behaviour. Integration of the equations yields results which are carefully discussed and which indicate how useful information may be obtained from the study. The studies include planar mechanisms, heavy equipment, automobile crash simulation and a spatial planetary system example. Research students, scientists and engineers will appreciate the practical approach taken in this book.

Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs--and the requirement for rapid solution--pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Audience: readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in "offline" optimization contexts and are interested in moving to "online" optimization.

We describe and compare several algorithms for approximating the solution to a model in" which inequality constraints occasionally bind. Their performance is evaluated and compared" using various parameterizations of the one sector growth model with irreversible investment. We" develop parameterized expectation algorithms which, on the basis of speed convenience of implementation, appear to dominate the other algorithms."

This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.

Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.