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Numerical Treatment of Partial Differential Equations
In 1988 we started work on the frst German edition of our book, which appeared in 1992. Our aim was to give students a textbook that contained the basic concepts and ideas behind most numerical methods for partial di?er- tial equations. The success of this frst edition and the second edition in 1994 encouraged us, ten years later, to write an almost completely new version, taking into account comments from colleagues and students and drawing on the enormous progress made in the numerical analysis of partial di?erential equations in recent times. The present English version slightly improves the third German edition of 2005: we have corrected some minor errors and added additional material and references.
Numerical Techniques for Chemical and Biological Engineers Using MATLAB® : A Simple Bifurcation Approach
This book addresses the bifurcation characteristics of chemical and biological processes as the general case and treats systems with a unique steady state as special cases. It uses a system approach which is the most efficient for knowledge organization and transfer. The book develops mathematical models for many commercial processes utilizing the mass-, momentum-, and heat-balance equations coupled to the rates of the processes that take place within the boundaries of the system. The models are solved numerically through MATLAB codes with emphasis on the design and optimization of the chemical and biological industrial equipment and plants.
Numerical solution of Variational Inequalities by Adaptive Finite Elements
Franz-Theo Suttmeier describes a general approach to a posteriori error estimation and adaptive mesh design for finite element models where the solution is subjected to inequality constraints. This is an extension to variational inequalities of the so-called Dual-Weighted-Residual method (DWR method) which is based on a variational formulation of the problem and uses global duality arguments for deriving weighted a posteriori error estimates with respect to arbitrary functionals of the error. In these estimates local residuals of the computed solution are multiplied by sensitivity factors which are obtained from a numerically computed dual solution. The resulting local error indicators are used in a feed-back process for generating economical meshes which are tailored according to the particular goal of the computation.
Numerical Solution of Partial Differential Equations on Parallel Computers
The scientific fields of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.
Numerical Simulation of Mechatronic Sensors and Actuators
The second edition of this book fully preserves the character of the first edition to combine the detailed physical modeling of mechatronic systems and their precise numerical simulation using the Finite Element (FE) method. Most of the text and general appearance of the previous edition were retained, while the coverage was extended and the presentation improved. A large part of the book describes the application of the developed numerical calculation schemes to industrial problems, e.g.: analysis and optimization of electrodynamic loudspeakers. In these parts, new computational methods are included, and last but not least, this new edition contains a new chapter on computational aeroacoustics to study the complex phenomenon of flow induced noise.
Numerical Simulation in Molecular Dynamics : Numerics, Algorithms, Parallelization, Applications
Particle models play an important role in many applications in physics, chemistry and biology. They can be studied on the computer with the help of molecular dynamics simulations. This book presents in detail both the necessary numerical methods and techniques (linked-cell method, SPME-method, tree codes, multipole technique) and the theoretical background and foundations. It illustrates the aspects modelling, discretization, algorithms and their parallel implementation with MPI on computer systems with distributed memory. Furthermore, detailed explanations are given to the different steps of numerical simulation, and code examples are provided.
Numerical partial differential equations for environmental scientists and engineers : A first practical course
This book concerns the practical solution of Partial Differential Equations (PDEs). It reflects an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It assumes the reader has gained some intuitive knowledge of PDE solution properties and now wants to solve some for real, in the context of practical problems arising in real situations. The practical aspect of this book is the infused focus on computation. It presents two major discretization methods - Finite Difference and Finite Element. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems. It is divided into three parts. Part I is an overview of Finite Difference Methods. Part II focuses on Finite Element Methods, including an FEM tutorial. Part III deals with Inverse Methods, introducing formal approaches to practical problems which are ill-posed.
Numerical Optimization : Theoretical and Practical Aspects
This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. Most of the algorithms are explained in a detailed manner, allowing straightforward implementation. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions. It's contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical, description, when coming to actual implementation. Besides, the nonsmooth optimization part has been substantially reorganized and expanded.
Numerical Optimization
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.The book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises.
Numerical Methods Using Java : For Data Science, Analysis, and Engineering
Covers a wide range of topics, including chapters on linear algebra, root finding, curve fitting, differentiation and integration, solving differential equations, random numbers and simulation, a whole suite of unconstrained and constrained optimization algorithms, statistics, regression and time series analysis. The mathematical concepts behind the algorithms are clearly explained, with plenty of code examples and illustrations to help even beginners get started. You will: Program in Java using a high-performance numerical library / Learn the mathematics for a wide range of numerical computing algorithms / Convert ideas and equations into code / Put together algorithms/ and classes to build your own engineering solution / Build solvers for industrial optimization problems / Do data analysis using basic and advanced statistics
Numerical Methods in Finance
The use of mathematical models and numerical techniques in finance is a growing practice, and an increasing number of applied mathematicians are working on applications in finance and business. This book presents some exciting developments arising from the combination of mathematics, numerical analysis, and finance. It covers a wide range of topics, from portfolio management and asset pricing, to performance, risk, debt and real option evaluation. It also presents applications of a variety of cutting edge approaches and techniques, including robust control, min-max optimisation, Bessel processes, stochastic viability, variational inequalities, and Monte-Carlo test techniques. The book also presents surveys of models and approaches in specific areas in finance, such as corporate debt valuation and portfolio selection
Numerical methods in computational finance : A partial differential equation (PDE/FDM) approach
This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance.
Numerical Methods for Nonsmooth Dynamical Systems : Applications in Mechanics and Electronics
This book concerns the numerical simulation of dynamical systems whose trajectories may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, firstly because of the many applications in which nonsmooth models are useful, secondly because they give rise to new problems in various fields of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution variational inequalities, each of these classes being itself split into several subclasses.
Numerical Methods for Laplace Transform Inversion
Operational methods have been used for over a century to solve many problems—for example, ordinary and partial differential equations. In many problems it is fairly easy to obtain the Laplace transform, but it can be very demanding to determine the inverse Laplace transform that is the solution of the given problem. Sometimes, after some difficult contour integration, we find that a series solution results, but even this may be quite difficult to evaluate in order to get an answer at a particular time value.
Numerical Methods for General and Structured Eigenvalue Problems
The purpose of this book is to describe recent developments in solving eig- value problems, in particular with respect to the QR and QZ algorithms as well as structured matrices. Outline Mathematically speaking, the eigenvalues of a square matrix A are the roots of its characteristic polynomial det(A??I). An invariant subspace is a linear subspace that stays invariant under the action of A. In realistic applications, it usually takes a long process of simpli?cations, linearizations and discreti- tions before one comes up with the problem of computing the eigenvalues of a matrix. In some cases, the eigenvalues have an intrinsic meaning, e.g., for the expected long-time behavior of a dynamical system; in others they are just meaningless intermediate values of a computational method. The same applies to invariant subspaces, which for example can describe sets of initial states for which a dynamical system produces exponentially decaying states. Computing eigenvalues has a long history, dating back to at least 1846 when Jacobi [172] wrote his famous paper on solving symmetric eigenvalue problems. Detailed historical accounts of this subject can be found in two papers by Golub and van der Vorst [140, 327].
Numerical Methods for Controlled Stochastic Delay Systems
The Markov chain approximation methods are widely used for the numerical solution of nonlinear stochastic control problems in continuous time. This book extends the methods to stochastic systems with delays. Because such problems are infinite-dimensional, many new issues arise in getting good numerical approximations and in the convergence proofs. Useful forms of numerical algorithms and system approximations are developed in this work, and the convergence proofs are given. All of the usual cost functions are treated as well as singular and impulsive controls. A major concern is on representations and approximations that use minimal memory.
Numerical Methods and Applications ; 6th International Conference, NMA 2006, Borovets, Bulgaria, August 20-24, 2006, Revised Papers
This book constitutes the thoroughly refereed post-proceedings of the 6th International Conference on Numerical Methods and Applications, NMA 2006. The papers are organized in topical sections on numerical methods for hyperbolic problems, robust preconditioning solution methods, Monte Carlo and quasi-Monte Carlo for diverse applications, metaheuristics for optimization problems, uncertain/control systems and reliable numerics, interpolation and quadrature processes, large-scale computations in environmental modelling, and contributed talks.
Numerical Mathematics and Advanced Applications ENUMATH 2019 ; European Conference, Egmond aan Zee, The Netherlands, September 30 - October 4
It contians basic aspects and new trends in numerical mathematics and scientific and industrial applications, all examined at the highest level of international expertise.
Numerical Mathematics and Advanced Applications ; Proceedings of ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007
The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of meetings held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. These proceedings contain a selection of invited plenary lectures, papers presented in minisymposia and contributed papers. Topics include theoretical aspects of new numerical techniques and algorithms as well as of applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scientific computing and their applications.
Numerical Mathematics and Advanced Applications ; Proceedings of ENUMATH 2005 the 6th European Conference on Numerical Mathematics and Advanced Applications, Santiago de Compostela, Spain, July 2005
This book include applications such as atmosphere and ocean, water pollution, electromagnetism, interface problems, waves, finance, heat transfer, unbounded domains, numerical linear algebra, convection-diffusion, fluid-structure, plates, solids, hyperbolic equations, multiphase flow, Navier-Stokes, singular perturbation problems, non linear PDE, control, parabolic equations, as well as methodologies such as a posteriori error estimates, discontinuous Galerkin methods, multiscale methods, optimization, adaptive methods, domain decomposition techniques, exponential integrators, hp-finite elements, level set methods, fractional step methods, penalty procedures, and finite volumes. The book gives an extensive overview of the most recent research in scientific computing, providing to the reader the latest developments concerning the mathematical issues and the applications of this active field of science.
