Numerical Methods For Evolutionary Differential Equations

Numerical Methods For Evolutionary Differential Equations Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Numerical Methods For Evolutionary Differential Equations book. This book definitely worth reading, it is an incredibly well-written.

Numerical Methods for Evolutionary Differential Equations

Uri M. Ascher
Numerical Methods for Evolutionary Differential Equations Book PDF

Author : Uri M. Ascher
Publisher : SIAM
Page : 404 pages
File Size : 42,8 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780898718911

Get Book

Numerical Methods for Evolutionary Differential Equations by Uri M. Ascher Pdf

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.

Handbook of Differential Equations: Evolutionary Equations

C.M. Dafermos,Eduard Feireisl
Handbook of Differential Equations Evolutionary Equations Book PDF

Author : C.M. Dafermos,Eduard Feireisl
Publisher : Elsevier
Page : 676 pages
File Size : 43,5 Mb
Release : 2005-10-05
Category : Mathematics
ISBN : 0080461387

Get Book

Handbook of Differential Equations: Evolutionary Equations by C.M. Dafermos,Eduard Feireisl Pdf

The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today. . Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.

Numerical Methods for Differential Equations

J.R. Dormand
Numerical Methods for Differential Equations Book PDF

Author : J.R. Dormand
Publisher : CRC Press
Page : 385 pages
File Size : 50,7 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351083553

Get Book

Numerical Methods for Differential Equations by J.R. Dormand Pdf

With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.

Introduction to Numerical Methods for Time Dependent Differential Equations

Heinz-Otto Kreiss,Omar Eduardo Ortiz
Introduction to Numerical Methods for Time Dependent Differential Equations Book PDF

Author : Heinz-Otto Kreiss,Omar Eduardo Ortiz
Publisher : John Wiley & Sons
Page : 192 pages
File Size : 53,9 Mb
Release : 2014-04-24
Category : Mathematics
ISBN : 9781118838914

Get Book

Introduction to Numerical Methods for Time Dependent Differential Equations by Heinz-Otto Kreiss,Omar Eduardo Ortiz Pdf

Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided. Introduction to Numerical Methods for Time Dependent Differential Equations features: A step-by-step discussion of the procedures needed to prove the stability of difference approximations Multiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equations A simplified approach in a one space dimension Analytical theory for difference approximations that is particularly useful to clarify procedures Introduction to Numerical Methods for Time Dependent Differential Equations is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines.

Numerical Methods for Ordinary Differential Equations

David F. Griffiths,Desmond J. Higham
Numerical Methods for Ordinary Differential Equations Book PDF

Author : David F. Griffiths,Desmond J. Higham
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 41,8 Mb
Release : 2010-11-11
Category : Mathematics
ISBN : 9780857291486

Get Book

Numerical Methods for Ordinary Differential Equations by David F. Griffiths,Desmond J. Higham Pdf

Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com

Handbook of differential equations

M. Chipot,P. Quittner
Handbook of differential equations Book PDF

Author : M. Chipot,P. Quittner
Publisher : Unknown
Page : 616 pages
File Size : 44,5 Mb
Release : 2006
Category : Differential equations
ISBN : 044451743X

Get Book

Handbook of differential equations by M. Chipot,P. Quittner Pdf

This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Key features: - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics.

Numerical Solution of Partial Differential Equations

Gordon D. Smith
Numerical Solution of Partial Differential Equations Book PDF

Author : Gordon D. Smith
Publisher : Oxford University Press
Page : 356 pages
File Size : 49,6 Mb
Release : 1985
Category : Computers
ISBN : 0198596502

Get Book

Numerical Solution of Partial Differential Equations by Gordon D. Smith Pdf

Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.

Finite Difference Methods for Nonlinear Evolution Equations

Zhi-Zhong Sun,Qifeng Zhang,Guang-hua Gao
Finite Difference Methods for Nonlinear Evolution Equations Book PDF

Author : Zhi-Zhong Sun,Qifeng Zhang,Guang-hua Gao
Publisher : Walter de Gruyter GmbH & Co KG
Page : 432 pages
File Size : 45,6 Mb
Release : 2023-05-08
Category : Mathematics
ISBN : 9783110796018

Get Book

Finite Difference Methods for Nonlinear Evolution Equations by Zhi-Zhong Sun,Qifeng Zhang,Guang-hua Gao Pdf

Introduces recent research results of finite difference methods including important nonlinear evolution equations in applied science. The presented difference schemes include nonlinear difference schemes and linearized difference schemes. Features widely used nonlinear evolution equations such as Burgers equation, regular long wave equation, Schrodinger equation and more. Each PDE model includes details on efficiency, stability, and convergence.

Numerical Methods for Partial Differential Equations

William F. Ames
Numerical Methods for Partial Differential Equations Book PDF

Author : William F. Ames
Publisher : Academic Press
Page : 451 pages
File Size : 54,5 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080571300

Get Book

Numerical Methods for Partial Differential Equations by William F. Ames Pdf

This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation. Material on finite elements and finite differences have been merged, and now constitute equal partners Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods References have been updated, and reflect the additional material Self-contained nature of the Second Edition has been maintained Very suitable for PDE courses

Finite Difference Methods for Ordinary and Partial Differential Equations

Randall J. LeVeque
Finite Difference Methods for Ordinary and Partial Differential Equations Book PDF

Author : Randall J. LeVeque
Publisher : SIAM
Page : 356 pages
File Size : 46,5 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898717833

Get Book

Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque Pdf

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Evolutionary Equations

Christian Seifert
Evolutionary Equations Book PDF

Author : Christian Seifert
Publisher : Springer Nature
Page : 321 pages
File Size : 48,9 Mb
Release : 2022
Category : Differential equations
ISBN : 9783030893972

Get Book

Evolutionary Equations by Christian Seifert Pdf

This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed. The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.

Evolutionary Equations with Applications in Natural Sciences

Jacek Banasiak,Mustapha Mokhtar-Kharroubi
Evolutionary Equations with Applications in Natural Sciences Book PDF

Author : Jacek Banasiak,Mustapha Mokhtar-Kharroubi
Publisher : Springer
Page : 493 pages
File Size : 52,9 Mb
Release : 2014-11-07
Category : Mathematics
ISBN : 9783319113227

Get Book

Evolutionary Equations with Applications in Natural Sciences by Jacek Banasiak,Mustapha Mokhtar-Kharroubi Pdf

With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. Truly unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering.

Mathematical Analysis and Numerical Methods for Science and Technology

Robert Dautray,Jacques-Louis Lions
Mathematical Analysis and Numerical Methods for Science and Technology Book PDF

Author : Robert Dautray,Jacques-Louis Lions
Publisher : Springer Science & Business Media
Page : 760 pages
File Size : 54,5 Mb
Release : 1999-11-23
Category : Mathematics
ISBN : 3540661018

Get Book

Mathematical Analysis and Numerical Methods for Science and Technology by Robert Dautray,Jacques-Louis Lions Pdf

299 G(t), and to obtain the corresponding properties of its Laplace transform (called the resolvent of - A) R(p) = (A + pl)-l , whose existence is linked with the spectrum of A. The functional space framework used will be, for simplicity, a Banach space(3). To summarise, we wish to extend definition (2) for bounded operators A, i.e. G(t) = exp( - tA) , to unbounded operators A over X, where X is now a Banach space. Plan of the Chapter We shall see in this chapter that this enterprise is possible, that it gives us in addition to what is demanded above, some supplementary information in a number of areas: - a new 'explicit' expression of the solution; - the regularity of the solution taking into account some conditions on the given data (u , u1,f etc ... ) with the notion of a strong solution; o - asymptotic properties of the solutions. In order to treat these problems we go through the following stages: in § 1, we shall study the principal properties of operators of semigroups {G(t)} acting in the space X, particularly the existence of an upper exponential bound (in t) of the norm of G(t). In §2, we shall study the functions u E X for which t --+ G(t)u is differentiable.

Topological Approximation Methods for Evolutionary Problems of Nonlinear Hydrodynamics

Victor G. Zvyagin,Dmitry A. Vorotnikov
Topological Approximation Methods for Evolutionary Problems of Nonlinear Hydrodynamics Book PDF

Author : Victor G. Zvyagin,Dmitry A. Vorotnikov
Publisher : Walter de Gruyter
Page : 245 pages
File Size : 53,7 Mb
Release : 2008-09-25
Category : Mathematics
ISBN : 9783110208283

Get Book

Topological Approximation Methods for Evolutionary Problems of Nonlinear Hydrodynamics by Victor G. Zvyagin,Dmitry A. Vorotnikov Pdf

The authors present functional analytical methods for solving a class of partial differential equations. The results have important applications to the numerical treatment of rheology (specific examples are the behaviour of blood or print colours) and to other applications in fluid mechanics. A class of methods for solving problems in hydrodynamics is presented.

High Order Nonlinear Numerical Schemes for Evolutionary PDEs

Rémi Abgrall,Héloïse Beaugendre,Pietro Marco Congedo,Cécile Dobrzynski,Vincent Perrier,Mario Ricchiuto
High Order Nonlinear Numerical Schemes for Evolutionary PDEs Book PDF

Author : Rémi Abgrall,Héloïse Beaugendre,Pietro Marco Congedo,Cécile Dobrzynski,Vincent Perrier,Mario Ricchiuto
Publisher : Springer
Page : 220 pages
File Size : 50,6 Mb
Release : 2014-05-19
Category : Mathematics
ISBN : 9783319054551

Get Book

High Order Nonlinear Numerical Schemes for Evolutionary PDEs by Rémi Abgrall,Héloïse Beaugendre,Pietro Marco Congedo,Cécile Dobrzynski,Vincent Perrier,Mario Ricchiuto Pdf

This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.