Collected Lectures On The Preservation Of Stability Under Discretization
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Collected Lectures On The Preservation Of Stability Under Discretization
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Author : Donald J. Estep
language : en
Publisher: SIAM
Release Date : 2002-01-01
Collected Lectures On The Preservation Of Stability Under Discretization written by Donald J. Estep and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
The 13 lectures are intended to be accessible to new graduate students of mathematics, sacrificing some detail in order to offer an accessible introduction to the fundamentals of stability that can provide a foundation for further study. Presenters from the US and Britain cover preserving qualitative stability features and structural stability, and investigating physical stability and model stability. Annotation copyrighted by Book News, Inc., Portland, OR
Spectral Methods For Time Dependent Problems
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Author : Jan S. Hesthaven
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-11
Spectral Methods For Time Dependent Problems written by Jan S. Hesthaven and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-11 with Mathematics categories.
Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.
Compatible Spatial Discretizations
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Author : Douglas N. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-26
Compatible Spatial Discretizations written by Douglas N. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-26 with Mathematics categories.
The IMA Hot Topics workshop on compatible spatialdiscretizations was held in 2004. This volume contains original contributions based on the material presented there. A unique feature is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Abstracts and presentation slides from the workshop can be accessed on the internet.
Implicit Explicit Methods For Evolutionary Partial Differential Equations
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Author : Sebastiano Boscarino
language : en
Publisher: SIAM
Release Date : 2024-12-12
Implicit Explicit Methods For Evolutionary Partial Differential Equations written by Sebastiano Boscarino and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-12 with Mathematics categories.
Implicit-explicit (IMEX) time discretization methods have proven to be highly effective for the numerical solution of a wide class of evolutionary partial differential equations (PDEs) across various contexts. These methods have become mainstream for solving evolutionary PDEs, particularly in the fields of hyperbolic and kinetic equations. The first book on the subject, Implicit-Explicit Methods for Evolutionary Partial Differential Equations provides an in-depth yet accessible approach. The authors summarize and illustrate the construction, analysis, and application of IMEX methods using examples, test cases, and implementation details; guide readers through the various methods and teach them how to select and use the one most appropriate for their needs; and demonstrate how to identify stiff terms and effectively implement high-order methods in time for a variety of systems of PDEs. Readers interested in learning modern techniques for the effective numerical solution of evolutionary PDEs with multiple time scales will find in this book a unified, compact, and accessible treatment. This book is intended for applied mathematicians, scientists, and engineers who use or are interested in learning about IMEX schemes. Readers should have some background in numerical methods for ODE systems and basic finite difference and finite volume discretization of evolutionary PDEs, along with a basic understanding of the relevant mathematical models. The book is suitable for students who have had a basic course in numerical analysis and are familiar with partial differential equations.
Parallel Computational Fluid Dynamics
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Author : Rupak Biswas
language : en
Publisher: DEStech Publications, Inc
Release Date : 2010
Parallel Computational Fluid Dynamics written by Rupak Biswas and has been published by DEStech Publications, Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
Handbook Of Numerical Methods For Hyperbolic Problems
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Author : Remi Abgrall
language : en
Publisher: Elsevier
Release Date : 2016-11-17
Handbook Of Numerical Methods For Hyperbolic Problems written by Remi Abgrall and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-17 with Mathematics categories.
Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations. - Provides detailed, cutting-edge background explanations of existing algorithms and their analysis - Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis - Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications - Written by leading subject experts in each field who provide breadth and depth of content coverage
Nonautonomous Dynamical Systems In The Life Sciences
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Author : Peter E. Kloeden
language : en
Publisher: Springer
Release Date : 2014-01-22
Nonautonomous Dynamical Systems In The Life Sciences written by Peter E. Kloeden and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-22 with Mathematics categories.
Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.
Acta Numerica 2003 Volume 12
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Author : Arieh Iserles
language : en
Publisher: Cambridge University Press
Release Date : 2003-09-15
Acta Numerica 2003 Volume 12 written by Arieh Iserles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-15 with Juvenile Nonfiction categories.
An annual volume presenting substantive survey articles in numerical mathematics and scientific computing.
Attractivity And Bifurcation For Nonautonomous Dynamical Systems
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Author : Martin Rasmussen
language : en
Publisher: Springer
Release Date : 2007-05-26
Attractivity And Bifurcation For Nonautonomous Dynamical Systems written by Martin Rasmussen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-26 with Mathematics categories.
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions.
Finite Element Methods For Incompressible Flow Problems
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Author : Volker John
language : en
Publisher: Springer
Release Date : 2016-10-27
Finite Element Methods For Incompressible Flow Problems written by Volker John and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-27 with Mathematics categories.
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.