Author : Bertil Gustafsson
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 21,91 MB
Release : 2007-12-06
Category : Mathematics
ISBN : 3540749934
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.
Author : Randall J. LeVeque
Publisher : SIAM
Page : 356 pages
File Size : 50,20 MB
Release : 2007-01-01
Category : Mathematics
ISBN : 9780898717839
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.
Author : Bertil Gustafsson
Publisher : John Wiley & Sons
Page : 464 pages
File Size : 39,80 MB
Release : 2013-07-18
Category : Mathematics
ISBN : 1118548523
Praise for the First Edition ". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations." —SIAM Review Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-dependent problems. The book treats differential equations and difference methods with a parallel development, thus achieving a more useful analysis of numerical methods. The Second Edition presents hyperbolic equations in great detail as well as new coverage on second-order systems of wave equations including acoustic waves, elastic waves, and Einstein equations. Compared to first-order hyperbolic systems, initial-boundary value problems for such systems contain new properties that must be taken into account when analyzing stability. Featuring the latest material in partial differential equations with new theorems, examples, and illustrations,Time-Dependent Problems and Difference Methods, Second Edition also includes: High order methods on staggered grids Extended treatment of Summation By Parts operators and their application to second-order derivatives Simplified presentation of certain parts and proofs Time-Dependent Problems and Difference Methods, Second Edition is an ideal reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs and to predict and investigate physical phenomena. The book is also excellent for graduate-level courses in applied mathematics and scientific computations.
Author : Robert M. Kirby
Publisher : Springer
Page : 504 pages
File Size : 33,18 MB
Release : 2015-11-26
Category : Computers
ISBN : 3319198009
The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2014), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of papers will provide the reader with a snapshot of the state-of-the-art and help initiate new research directions through the extensive biography.
Author : Jan S. Hesthaven
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 15,37 MB
Release : 2010-10-29
Category : Mathematics
ISBN : 3642153372
The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.
Author : Martin Kronbichler
Publisher : Springer Nature
Page : 314 pages
File Size : 47,84 MB
Release : 2021-01-04
Category : Technology & Engineering
ISBN : 3030606104
The book introduces modern high-order methods for computational fluid dynamics. As compared to low order finite volumes predominant in today's production codes, higher order discretizations significantly reduce dispersion errors, the main source of error in long-time simulations of flow at higher Reynolds numbers. A major goal of this book is to teach the basics of the discontinuous Galerkin (DG) method in terms of its finite volume and finite element ingredients. It also discusses the computational efficiency of high-order methods versus state-of-the-art low order methods in the finite difference context, given that accuracy requirements in engineering are often not overly strict. The book mainly addresses researchers and doctoral students in engineering, applied mathematics, physics and high-performance computing with a strong interest in the interdisciplinary aspects of computational fluid dynamics. It is also well-suited for practicing computational engineers who would like to gain an overview of discontinuous Galerkin methods, modern algorithmic realizations, and high-performance implementations.
Author :
Publisher : Bookboon
Page : 144 pages
File Size : 38,73 MB
Release :
Category :
ISBN : 8776816427
Author : Jan S. Hesthaven
Publisher : Cambridge University Press
Page : 284 pages
File Size : 32,50 MB
Release : 2007-01-11
Category : Mathematics
ISBN : 9780521792110
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.
Author : Zhilin Li
Publisher : Cambridge University Press
Page : 305 pages
File Size : 21,89 MB
Release : 2017-11-30
Category : Mathematics
ISBN : 1107163226
A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
Author : Marco L. Bittencourt
Publisher : Springer
Page : 681 pages
File Size : 25,93 MB
Release : 2017-11-07
Category : Mathematics
ISBN : 3319658700
This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
