Kategoria BISAC: Mathematics >> Numerical Analysis

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a...

This series of volumes will cover all the major aspects of Numerical Analysis, serving as the basic reference work on the subject. Each volume will concentrate on one, or two, particular topics and will be essentially self-contained. Each article, written by an expert, is an in-depth survey, reflecting the most recent trends in the field. The Handbook will cover the basic methods of Numerical Analysis, under the following general headings: # Solution of Equations in R n # Finite Difference Methods # Finite Element Methods # Techniques of Scientific Computing # Optimization Theory and...

The use of computers and computational methods has become ubiquitous in biological and biomedical research. During the last 2 decades most basic algorithms have not changed, but what has is the huge increase in computer speed and ease of use, along with the corresponding orders of magnitude decrease in cost.

A general perception exists that the only applications of computers and computer methods in biological and biomedical research are either basic statistical analysis or the searching of DNA sequence data bases. While these are important applications they only scratch the surface...

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing...

Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board.

• Over 500 numerical algorithms, their fundamental principles, and...

"Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems.

This book incorporates diverse perspectives from broad-ranging areas of research including,...

This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and fast multipole method.

ECM2 is a completely updated and expanded Second Edition of the well-established Encyclopedia of Computational Mechanics. The project has once again been prepared under the guidance of three of the world's foremost experts in the field:

• Erwin Stein, Professor Emeritus, Stein Institut fUr Baumechanik und Numerische Mechanik, Leibniz UniversitAt, Hannover, Germany
• RenE de Borst, Centenary Professor of Civil Engineering, University of Sheffield, UK
• Thomas J. R. Hughes, Peter O'Donnell Jr. Chair in Computational and Applied Mathematics and Professor of Aerospace...

Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems.
This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of...

This book contains theoretical and application-oriented methods to treat models of dynamical systems involving non-smooth nonlinearities.
The theoretical approach that has been retained and underlined in this work is associated with differential inclusions of mainly finite dimensional dynamical systems and the introduction of maximal monotone operators (graphs) in order to describe models of impact or friction. The authors of this book master the mathematical, numerical and modeling tools in a particular way so that they can propose all aspects of the approach, in both a...