Strong Stability Preserving Runge Kutta And Multistep Time Discretizations

Author : Sigal Gottlieb,David I. Ketcheson,Chi-Wang Shu
Publisher : World Scientific
Page : 189 pages
File Size : 49,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814289269

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Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations by Sigal Gottlieb,David I. Ketcheson,Chi-Wang Shu Pdf

This book captures the state-of-the-art in the field of Strong Stability Preserving (SSP) time stepping methods, which have significant advantages for the time evolution of partial differential equations describing a wide range of physical phenomena. This comprehensive book describes the development of SSP methods, explains the types of problems which require the use of these methods and demonstrates the efficiency of these methods using a variety of numerical examples. Another valuable feature of this book is that it collects the most useful SSP methods, both explicit and implicit, and presents the other properties of these methods which make them desirable (such as low storage, small error coefficients, large linear stability domains). This book is valuable for both researchers studying the field of time-discretizations for PDEs, and the users of such methods.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 51,9 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9789814466479

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Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations by Anonim Pdf

Author : Sigal Gottlieb,Institute for Computer Applications in Science and Engineering
Publisher : Unknown
Page : 30 pages
File Size : 52,9 Mb
Release : 2000
Category : Boundary element methods
ISBN : NASA:31769000711369

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Strong Stability Preserving High-order Time Discretization Methods by Sigal Gottlieb,Institute for Computer Applications in Science and Engineering Pdf

In this paper we review and further develop a class of strong-stability preserving (SSP) high-order time discretizations for semi-discrete method-of-lines approximations of partial differential equations. Termed TVD (total variation diminishing) time discretizations before this class of high-order time discretization methods preserves the strong-stability properties of first-order Euler time stepping and has proved very useful especially in solving hyperbolic partial differential equations. The new contributions in this paper include the development of optimal explicit SSP linear Runge-Kutta methods, their application to the strong stability of coercive approximations, a systematic study of explicit SSP multi-step methods, and a study of the strong-stability preserving property of implicit Runge-Kutta and multi-step methods.

Author : Willem Hundsdorfer,Jan G. Verwer
Publisher : Springer Science & Business Media
Page : 479 pages
File Size : 45,5 Mb
Release : 2013-04-17
Category : Technology & Engineering
ISBN : 9783662090176

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Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by Willem Hundsdorfer,Jan G. Verwer Pdf

Unique book on Reaction-Advection-Diffusion problems

Author : David Hart
Publisher : Unknown
Page : 128 pages
File Size : 54,8 Mb
Release : 2017-07-09
Category : Electronic
ISBN : 1450352723

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Proceedings of the Practice and Experience in Advanced Research Computing 2017 on Sustainability, Success and Impact by David Hart Pdf

Practice and Experience in Advanced Research Computing 2017 Jul 09, 2017-Jul 13, 2017 New Orleans, USA. You can view more information about this proceeding and all of ACM�s other published conference proceedings from the ACM Digital Library: http://www.acm.org/dl.

Author : Christopher Alan Kennedy
Publisher : Unknown
Page : 56 pages
File Size : 54,9 Mb
Release : 2001
Category : Differential equations
ISBN : NASA:31769000643307

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Additive Runge-Kutta Schemes for Convection-diffusion-reaction Equations by Christopher Alan Kennedy Pdf

Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations. First, accuracy, stability, conservation, and dense output are considered for the general case when N different Runge-Kutta methods are grouped into a single composite method. Then, implicit-explicit, N=2, additive Runge-Kutta ARK methods from third- to fifth-order are presented that allow for integration of stiff terms by an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge-Kutta (ESDIRK) method while the nonstiff terms are integrated with a traditional explicit Runge-Kutta method (ERK). Coupling error terms are of equal order to those of the elemental methods. Derived ARK methods have vanishing stability functions for very large values of the stiff scaled eigenvalue and retain high stability efficiency in the absence of stiffness.

Author : Arieh Iserles
Publisher : Cambridge University Press
Page : 481 pages
File Size : 45,5 Mb
Release : 2008-11-27
Category : Mathematics
ISBN : 9781139473767

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A First Course in the Numerical Analysis of Differential Equations by Arieh Iserles Pdf

Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.

Author : Ronald E. Mickens
Publisher : World Scientific
Page : 268 pages
File Size : 49,5 Mb
Release : 2000
Category : Mathematics
ISBN : 981024133X

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Applications of Nonstandard Finite Difference Schemes by Ronald E. Mickens Pdf

The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter I gives an overview of the subject and summarizes previous work. Chapters 2 and 3 consider in detail the construction and numerical implementation of schemes for physical problems involving convection-diffusion-reaction equations, that arise in groundwater pollution and scattering of electromagnetic waves using Maxwell's equations. Chapter 4 examines certain mathematical issues related to the nonstandard discretization of competitive and cooperative models for ecology. The application chapters illustrate well the power of nonstandard methods. In particular, for the same accuracy as obtained by standard techniques, larger step sizes can be used. This volume will satisfy the needs of scientists, engineers, and mathematicians who wish to know how to construct nonstandard schemes and see how these are applied to obtain numerical solutions of the differential equations which arise in the study of nonlinear dynamical systems modeling important physical phenomena.

Author : H. Lomax,Thomas H. Pulliam,David W. Zingg
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 45,7 Mb
Release : 2013-03-09
Category : Science
ISBN : 9783662046548

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Fundamentals of Computational Fluid Dynamics by H. Lomax,Thomas H. Pulliam,David W. Zingg Pdf

The chosen semi-discrete approach of a reduction procedure of partial differential equations to ordinary differential equations and finally to difference equations gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.

Author : Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642597213

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Discontinuous Galerkin Methods by Bernardo Cockburn,George E. Karniadakis,Chi-Wang Shu Pdf

A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.

Author : Jacques-Louis Lions,Ta-ch'ien Li,Daqian Li
Publisher : World Scientific
Page : 316 pages
File Size : 46,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9812562265

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Frontiers in Mathematical Analysis and Numerical Methods by Jacques-Louis Lions,Ta-ch'ien Li,Daqian Li Pdf

This invaluable volume is a collection of articles in memory ofJacques-Louis Lions, a leading mathematician and the founder of theContemporary French Applied Mathematics School. The contributions havebeen written by his friends, colleagues and students, including CBardos, A Bensoussan, S S Chern, P G Ciarlet, R Glowinski, Gu Chaohao, B Malgrange, G Marchuk, O Pironneau, W Strauss, R Temam, etc

Author : Xin-She Yang
Publisher : World Scientific Publishing Company
Page : 344 pages
File Size : 44,9 Mb
Release : 2014-11-26
Category : Mathematics
ISBN : 9789814635806

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Introduction to Computational Mathematics by Xin-She Yang Pdf

This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of contemporary numerical algorithms, scientific computing and optimization. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. This edition covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithm, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, nonlinear curve-fitting to data modelling, bio-inspired algorithms and swarm intelligence. This book is especially suitable for both undergraduates and graduates in computational mathematics, numerical algorithms, scientific computing, mathematical programming, artificial intelligence and engineering optimization. Thus, it can be used as a textbook and/or reference book.

Author : Remi Abgrall,Chi-Wang Shu
Publisher : Elsevier
Page : 666 pages
File Size : 42,6 Mb
Release : 2016-11-17
Category : Mathematics
ISBN : 9780444637956

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Handbook of Numerical Methods for Hyperbolic Problems by Remi Abgrall,Chi-Wang Shu Pdf

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

Author : Peter H. Lauritzen,Christiane Jablonowski,Mark A. Taylor,Ramachandran D. Nair
Publisher : Springer Science & Business Media
Page : 570 pages
File Size : 50,7 Mb
Release : 2011-03-29
Category : Mathematics
ISBN : 9783642116407

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Numerical Techniques for Global Atmospheric Models by Peter H. Lauritzen,Christiane Jablonowski,Mark A. Taylor,Ramachandran D. Nair Pdf

This book surveys recent developments in numerical techniques for global atmospheric models. It is based upon a collection of lectures prepared by leading experts in the field. The chapters reveal the multitude of steps that determine the global atmospheric model design. They encompass the choice of the equation set, computational grids on the sphere, horizontal and vertical discretizations, time integration methods, filtering and diffusion mechanisms, conservation properties, tracer transport, and considerations for designing models for massively parallel computers. A reader interested in applied numerical methods but also the many facets of atmospheric modeling should find this book of particular relevance.

Author : Miller John J H,O'riordan Eugene,Shishkin G I
Publisher : World Scientific
Page : 192 pages
File Size : 42,7 Mb
Release : 2012-02-29
Category : Mathematics
ISBN : 9789814452779

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Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition) by Miller John J H,O'riordan Eugene,Shishkin G I Pdf

Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.