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“…a timely contribution to a field of growing importance. This carefully edited book presents a rich collection of chapters ranging from mathematical methodology to emerging applications. I recommend it to students as a rigorous and comprehensive presentation of simulation-based optimization and to researchers as an overview of recent advances and challenges in the field.” — Jorge Nocedal, Professor, Northwestern University.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—pos...
Equation-based object-oriented (EOO) modeling languages such as Modelica provide a convenient, declarative method for describing models of cyber-physical systems. Because of the ease of use of EOO languages, large and complex models can be built with limited effort. However, current state-of-the-art tools do not provide the user with enough information when errors appear or simulation results are wrong. It is of paramount importance that such tools should give the user enough information to correct errors or understand where the problems that lead to wrong simulation results are located. However, understanding the model translation process of an EOO compiler is a daunting task that not only ...
This book offers the first comprehensive account of how the logarithmic norm is used for matrices, nonlinear maps and linear differential operators, with a focus on initial and boundary value problems. Complementing the usual operator norm, the logarithmic norm is a versatile tool which provides unique additional information on the magnitude of an operator. It is instrumental in the stability theory of dynamical systems and in the theory of elliptic operator equations. The text adopts a unified approach to address a wide range of themes in applied mathematics. It explores the role of the logarithmic norm in scientific computing, compares the operator bounds with those of spectral theory, and illustrates the theory with classical models from science and engineering. Many previously unpublished results are presented alongside established material, supporting researchers in applied mathematics and computational engineering who seek a systematic approach to stability and perturbation bounds in initial value problems, boundary value problems and partial differential equations. Primarily intended as a reference text, the book can also serve as a graduate text for PhD students.
Highly computer-oriented text, introducing numerical methods and algorithms along with the applications and conceptual tools. Includes homework problems, suggestions for research projects, and open-ended questions at the end of each chapter. Written by our successful author who also wrote Continuous System Modeling, a best-selling Springer book first published in the 1991 (sold about 1500 copies).
This volume contains the proceedings of the Second International Workshop on Hybrid Systems: Computation and Control (HSCC’99) to be held March 29- 31, 1999, in the village Berg en Dal near Nijmegen, The Netherlands. The rst workshop of this series was held in April 1998 at the University of California at Berkeley. The series follows meetings that were initiated by Anil Nerode at Cornell University. The proceedings of those meetings were published in the Springer-Verlag LNCS Series, Volumes 736, 999, 1066, 1201, and 1273. The p- ceedings of the rst workshop of the new series was published in LNCS 1386. The focus of the workshop is on modeling, control, synthesis, design, and ve- cation of ...
This volume addresses some of the research areas in the general field of stability studies for differential equations, with emphasis on issues of concern for numerical studies. Topics considered include: (i) the long time integration of Hamiltonian Ordinary DEs and highly oscillatory systems, (ii) connection between stochastic DEs and geometric integration using the Markov chain Monte Carlo method, (iii) computation of dynamic patterns in evolutionary partial DEs, (iv) decomposition of matrices depending on parameters and localization of singularities, and (v) uniform stability analysis for time dependent linear initial value problems of ODEs. The problems considered in this volume are of interest to people working on numerical as well as qualitative aspects of differential equations, and it will serve both as a reference and as an entry point into further research.
Fritzson covers the Modelica language in impressive depth from the basic concepts such as cyber-physical, equation-base, object-oriented, system, model, and simulation, while also incorporating over a hundred exercises and their solutions for a tutorial, easy-to-read experience. The only book with complete Modelica 3.3 coverage Over one hundred exercises and solutions Examines basic concepts such as cyber-physical, equation-based, object-oriented, system, model, and simulation
This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
This book project was initiated at The Tribute Workshop in Honour of Gunnar Sparr and the follow-up workshop Inequalities, Interpolation, Non-commutative, Analysis, Non-commutative Geometry and Applications INANGA08, held at the Centre for Mathematical Sciences, Lund University in May and November of 2008. The resulting book is dedicated in celebration of Gunnar Sparr's sixty-fifth anniversary and more than forty years of exceptional service to mathematics and its applications in engineering and technology, mathematics and engineering education, as well as interdisciplinary, industrial and international cooperation. This book presents new advances in several areas of mathematics and engineer...