Numerical Methods For Evolutionary Differential Equations
DOWNLOAD
Download Numerical Methods For Evolutionary Differential Equations PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Numerical Methods For Evolutionary Differential Equations book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Numerical Methods For Evolutionary Differential Equations
DOWNLOAD
Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 2008-01-01
Numerical Methods For Evolutionary Differential Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. Audience: suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method.
Implicit Explicit Methods For Evolutionary Partial Differential Equations
DOWNLOAD
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.
Handbook Of Differential Equations Evolutionary Equations
DOWNLOAD
Author : C.M. Dafermos
language : en
Publisher: Elsevier
Release Date : 2008-10-06
Handbook Of Differential Equations Evolutionary Equations written by C.M. Dafermos and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-06 with Mathematics categories.
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.- Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts
Integral Equation Methods For Evolutionary Pde
DOWNLOAD
Author : Lehel Banjai
language : en
Publisher: Springer Nature
Release Date : 2022-11-08
Integral Equation Methods For Evolutionary Pde written by Lehel Banjai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-08 with Mathematics categories.
This book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method. Properties of convolution quadrature, based on both linear multistep and Runge–Kutta methods, are explained in detail, always with wave propagation problems in mind. Main algorithms for implementing the discrete schemes are described and illustrated by short Matlab codes; translation to other languages can be found on the accompanying GitHub page. The codes are used to present numerous numerical examples to give the reader a feeling for the qualitative behaviour of the discrete schemes in practice. Applications to acoustic and electromagnetic scattering are described with an emphasis on the acoustic case where the fully discrete schemes for sound-soft and sound-hard scattering are developed and analysed in detail. A strength of the book is that more advanced applications such as linear and non-linear impedance boundary conditions and FEM/BEM coupling are also covered. While the focus is on wave scattering, a chapter on parabolic problems is included which also covers the relevant fast and oblivious algorithms. Finally, a brief description of data sparse techniques and modified convolution quadrature methods completes the book. Suitable for graduate students and above, this book is essentially self-contained, with background in mathematical analysis listed in the appendix along with other useful facts. Although not strictly necessary, some familiarity with boundary integral equations for steady state problems is desirable.
Essential Partial Differential Equations
DOWNLOAD
Author : David F. Griffiths
language : en
Publisher: Springer
Release Date : 2015-09-24
Essential Partial Differential Equations written by David F. Griffiths and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-24 with Mathematics categories.
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.
Methods In Computational Science
DOWNLOAD
Author : Johan Hoffman
language : en
Publisher: SIAM
Release Date : 2021-10-19
Methods In Computational Science written by Johan Hoffman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-19 with Computers categories.
Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms, with the aim of familiarizing the reader with the field’s theoretical foundations and providing the practical skills to use and develop computational methods. Centered around a set of fundamental algorithms presented in the form of pseudocode, this self-contained textbook extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing. It presents theoretical material alongside several examples and exercises and provides Python implementations of many key algorithms. Methods in Computational Science is for advanced undergraduate and graduate-level students studying computer science and data science. It can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science. It is appropriate for courses in advanced numerical analysis, data science, numerical optimization, and approximation theory.
Mathematical Foundations Of Finite Elements And Iterative Solvers
DOWNLOAD
Author : Paolo Gatto
language : en
Publisher: SIAM
Release Date : 2022-06-27
Mathematical Foundations Of Finite Elements And Iterative Solvers written by Paolo Gatto and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-27 with Mathematics categories.
“This book combines an updated look, at an advanced level, of the mathematical theory of the finite element method (including some important recent developments), and a presentation of many of the standard iterative methods for the numerical solution of the linear system of equations that results from finite element discretization, including saddle point problems arising from mixed finite element approximation. For the reader with some prior background in the subject, this text clarifies the importance of the essential ideas and provides a deeper understanding of how the basic concepts fit together.” — Richard S. Falk, Rutgers University “Students of applied mathematics, engineering, and science will welcome this insightful and carefully crafted introduction to the mathematics of finite elements and to algorithms for iterative solvers. Concise, descriptive, and entertaining, the text covers all of the key mathematical ideas and concepts dealing with finite element approximations of problems in mechanics and physics governed by partial differential equations while interweaving basic concepts on Sobolev spaces and basic theorems of functional analysis presented in an effective tutorial style.” — J. Tinsley Oden, The University of Texas at Austin This textbook describes the mathematical principles of the finite element method, a technique that turns a (linear) partial differential equation into a discrete linear system, often amenable to fast linear algebra. Reflecting the author’s decade of experience in the field, Mathematical Foundations of Finite Elements and Iterative Solvers examines the crucial interplay between analysis, discretization, and computations in modern numerical analysis; furthermore, it recounts historical developments leading to current state-of-the-art techniques. While self-contained, this textbook provides a clear and in-depth discussion of several topics, including elliptic problems, continuous Galerkin methods, iterative solvers, advection-diffusion problems, and saddle point problems. Accessible to readers with a beginning background in functional analysis and linear algebra, this text can be used in graduate-level courses on advanced numerical analysis, data science, numerical optimization, and approximation theory. Professionals in numerical analysis and finite element methods will also find the book of interest.
Mastering Frequency Domain Techniques For The Stability Analysis Of Lti Time Delay Systems
DOWNLOAD
Author : Rifat Sipahi
language : en
Publisher: SIAM
Release Date : 2019-05-21
Mastering Frequency Domain Techniques For The Stability Analysis Of Lti Time Delay Systems written by Rifat Sipahi and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-21 with Science categories.
In many dynamical systems, time delays arise because of the time it takes to measure system states, perceive and evaluate events, formulate decisions, and act on those decisions. The presence of delays may lead to undesirable outcomes; without an engineered design, the dynamics may underperform, oscillate, and even become unstable. How to study the stability of dynamical systems influenced by time delays is a fundamental question. Related issues include how much time delay the system can withstand without becoming unstable and how to change system parameters to render improved dynamic characteristics, utilize or tune the delay itself to improve dynamical behavior, and assess the stability and speed of response of the dynamics. Mastering Frequency Domain Techniques for the Stability Analysis of LTI Time Delay Systems addresses these questions for linear time-invariant (LTI) systems with an eigenvalue-based approach built upon frequency domain techniques. Readers will find key results from the literature, including all subtopics for those interested in deeper exploration. The book presents step-by-step demonstrations of all implementations?including those that require special care in mathematics and numerical implementation?from the simpler, more intuitive ones in the introductory chapters to the more complex ones found in the later chapters. Maple and MATLAB code is available from the author?s website. This multipurpose book is intended for graduate students, instructors, and researchers working in control engineering, robotics, mechatronics, network control systems, human-in-the-loop systems, human-machine systems, remote control and tele-operation, transportation systems, energy systems, and process control, as well as for those working in applied mathematics, systems biology, and physics. It can be used as a primary text in courses on stability and control of time delay systems and as a supplementary text in courses in the above listed domains.
Library Of Congress Subject Headings
DOWNLOAD
Author : Library of Congress
language : en
Publisher:
Release Date : 2010
Library Of Congress Subject Headings written by Library of Congress and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Subject headings, Library of Congress categories.
Nonlocal Integral Equation Continuum Models
DOWNLOAD
Author : Marta D'Elia
language : en
Publisher: SIAM
Release Date : 2024-09-12
Nonlocal Integral Equation Continuum Models written by Marta D'Elia and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-12 with Mathematics categories.
The book presents the state of the art of nonlocal modeling and discretization and provides a practical introduction to nonlocal modeling for readers who are not familiar with such models. These models have recently become a viable alternative to classical partial differential equations when the latter are unable to capture effects such as discontinuities and multiscale behavior in a system of interest. Because of their integral nature, nonlocal operators allow for the relaxation of regularity requirements on the solution and thus allow for the capture of multiscale effects, the result of which is their successful use in many scientific and engineering applications. The book also provides a thorough analysis and numerical treatment of nonstandard nonlocal models, focusing on both well-known and nonstandard interaction neighborhoods. In addition, the book delivers an extensive practical treatment of the implementation of discretization strategies via finite element methods. Numerous figures are provided as concrete examples to illustrate both the analytic and computational results. Nonlocal Integral Equation Continuum Models: Nonstandard Interaction Neighborhoods and Finite Element Discretizations is intended for mathematical and application researchers interested in alternatives to using partial differential equation models that better describe the phenomena they are interested in. The book will also be of use to computational scientists and engineers who need to make sense of how to use available software, improve existing software, or develop new software tailored to their application interests.