Time Dependent Problems and Difference Methods

Author: Bertil Gustafsson
Publisher: John Wiley & Sons
ISBN: 9780471507345
Format: PDF, Docs
Download Now
Time dependent problems frequently pose challenges in areas of science and engineering dealing with numerical analysis, scientific computation, mathematical models, and most importantly—numerical experiments intended to analyze physical behavior and test design. Time Dependent Problems and Difference Methods addresses these various industrial considerations in a pragmatic and detailed manner, giving special attention to time dependent problems in its coverage of the derivation and analysis of numerical methods for computational approximations to Partial Differential Equations (PDEs). The book is written in two parts. Part I discusses problems with periodic solutions; Part II proceeds to discuss initial boundary value problems for partial differential equations and numerical methods for them. The problems with periodic solutions have been chosen because they allow the application of Fourier analysis without the complication that arises from the infinite domain for the corresponding Cauchy problem. Furthermore, the analysis of periodic problems provides necessary conditions when constructing methods for initial boundary value problems. Much of the material included in Part II appears for the first time in this book. The authors draw on their own interests and combined extensive experience in applied mathematics and computer science to bring about this practical and useful guide. They provide complete discussions of the pertinent theorems and back them up with examples and illustrations. For physical scientists, engineers, or anyone who uses numerical experiments to test designs or to predict and investigate physical phenomena, this invaluable guide is destined to become a constant companion. Time Dependent Problems and Difference Methods analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations.

Time Dependent Problems and Difference Methods

Author: Bertil Gustafsson
Publisher: John Wiley & Sons
ISBN: 1118548523
Format: PDF, Mobi
Download Now
Praise for the First Edition ". . . fills a considerable gap in the numerical analysisliterature by providing a self-contained treatment . . . this is animportant work written in a clear style . . . warmly recommended toany graduate student or researcher in the field of the numericalsolution of partial differential equations." —SIAM Review Time-Dependent Problems and Difference Methods, SecondEdition continues to provide guidance for the analysis ofdifference methods for computing approximate solutions to partialdifferential equations for time-dependent problems. The book treatsdifferential equations and difference methods with a paralleldevelopment, thus achieving a more useful analysis of numericalmethods. The Second Edition presents hyperbolic equations in greatdetail as well as new coverage on second-order systems of waveequations including acoustic waves, elastic waves, and Einsteinequations. Compared to first-order hyperbolic systems,initial-boundary value problems for such systems contain newproperties that must be taken into account when analyzingstability. Featuring the latest material in partial differentialequations with new theorems, examples, andillustrations,Time-Dependent Problems and Difference Methods,Second Edition also includes: High order methods on staggered grids Extended treatment of Summation By Parts operators and theirapplication to second-order derivatives Simplified presentation of certain parts and proofs Time-Dependent Problems and Difference Methods, SecondEdition is an ideal reference for physical scientists,engineers, numerical analysts, and mathematical modelers who usenumerical experiments to test designs and to predict andinvestigate physical phenomena. The book is also excellent forgraduate-level courses in applied mathematics and scientificcomputations.

High Order Difference Methods for Time Dependent PDE

Author: Bertil Gustafsson
Publisher: Springer Science & Business Media
ISBN: 9783540749936
Format: PDF
Download Now
This book covers high order finite difference methods for time dependent PDE. It gives an overview of the basic theory and construction principles by using model examples. The book also contains a general presentation of the techniques and results for well-posedness and stability, with inclusion of the three fundamental methods of analysis both for PDE in its original and discretized form: the Fourier transform, the eneregy method and the Laplace transform.

Finite Difference Methods for Ordinary and Partial Differential Equations

Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Format: PDF, ePub, Docs
Download Now
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.

Spectral Methods for Time Dependent Problems

Author: Jan S. Hesthaven
Publisher: Cambridge University Press
ISBN: 113945952X
Format: PDF, ePub, Mobi
Download Now
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.

Partielle Differentialgleichungen und numerische Methoden

Author: Stig Larsson
Publisher: Springer-Verlag
ISBN: 3540274227
Format: PDF, ePub, Mobi
Download Now
Das Buch ist für Studenten der angewandten Mathematik und der Ingenieurwissenschaften auf Vordiplomniveau geeignet. Der Schwerpunkt liegt auf der Verbindung der Theorie linearer partieller Differentialgleichungen mit der Theorie finiter Differenzenverfahren und der Theorie der Methoden finiter Elemente. Für jede Klasse partieller Differentialgleichungen, d.h. elliptische, parabolische und hyperbolische, enthält der Text jeweils ein Kapitel zur mathematischen Theorie der Differentialgleichung gefolgt von einem Kapitel zu finiten Differenzenverfahren sowie einem zu Methoden der finiten Elemente. Den Kapiteln zu elliptischen Gleichungen geht ein Kapitel zum Zweipunkt-Randwertproblem für gewöhnliche Differentialgleichungen voran. Ebenso ist den Kapiteln zu zeitabhängigen Problemen ein Kapitel zum Anfangswertproblem für gewöhnliche Differentialgleichungen vorangestellt. Zudem gibt es ein Kapitel zum elliptischen Eigenwertproblem und zur Entwicklung nach Eigenfunktionen. Die Darstellung setzt keine tiefer gehenden Kenntnisse in Analysis und Funktionalanalysis voraus. Das erforderliche Grundwissen über lineare Funktionalanalysis und Sobolev-Räume wird im Anhang im Überblick besprochen.

Time dependent Partial Differential Equations and Their Numerical Solution

Author: Heinz-Otto Kreiss
Publisher: Birkhäuser
ISBN: 3034882297
Format: PDF, Docs
Download Now
This book studies time-dependent partial differential equations and their numerical solution, developing the analytic and the numerical theory in parallel, and placing special emphasis on the discretization of boundary conditions. The theoretical results are then applied to Newtonian and non-Newtonian flows, two-phase flows and geophysical problems. This book will be a useful introduction to the field for applied mathematicians and graduate students.

Difference Methods for Initial Boundary Value Problems and Flow Around Bodies

Author: You-lan Zhu
Publisher: Springer Science & Business Media
ISBN: 3662067072
Format: PDF, Docs
Download Now
Since the appearance of computers, numerical methods for discontinuous solutions of quasi-linear hyperbolic systems of partial differential equations have been among the most important research subjects in numerical analysis. The authors have developed a new difference method (named the singularity-separating method) for quasi-linear hyperbolic systems of partial differential equations. Its most important feature is that it possesses a high accuracy even for problems with singularities such as schocks, contact discontinuities, rarefaction waves and detonations. Besides the thorough description of the method itself, its mathematical foundation (stability-convergence theory of difference schemes for initial-boundary-value hyperbolic problems) and its application to supersonic flow around bodies are discussed. Further, the method of lines and its application to blunt body problems and conical flow problems are described in detail. This book should soon be an important working basis for both graduate students and researchers in the field of partial differential equations as well as in mathematical physics.