Numerical Time Dependent Partial Differential Equations for Scientists and Engineers

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations

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  • Author : Moysey Brio
  • Publisher : Academic Press
  • Pages : 312 pages
  • ISBN : 9780080917047
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKNumerical Time Dependent Partial Differential Equations for Scientists and Engineers

Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers

Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers
  • Author : Moysey Brio,Gary M. Webb,Aramais R. Zakharian
  • Publisher : Academic Press
  • Release : 21 September 2010
GET THIS BOOKNumerical Time-Dependent Partial Differential Equations for Scientists and Engineers

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught

Numerical Partial Differential Equations for Environmental Scientists and Engineers

Numerical Partial Differential Equations for Environmental Scientists and Engineers
  • Author : Daniel R. Lynch
  • Publisher : Springer Science & Business Media
  • Release : 02 June 2006
GET THIS BOOKNumerical Partial Differential Equations for Environmental Scientists and Engineers

For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It presents two major discretization methods: Finite Difference and Finite Element, plus a section on practical approaches to ill-posed problems. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems.

Proper Orthogonal Decomposition Methods for Partial Differential Equations

Proper Orthogonal Decomposition Methods for Partial Differential Equations
  • Author : Zhendong Luo,Goong Chen
  • Publisher : Academic Press
  • Release : 26 November 2018
GET THIS BOOKProper Orthogonal Decomposition Methods for Partial Differential Equations

Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs,

Introduction to Numerical Methods for Time Dependent Differential Equations

Introduction to Numerical Methods for Time Dependent Differential Equations
  • Author : Heinz-Otto Kreiss,Omar Eduardo Ortiz
  • Publisher : John Wiley & Sons
  • Release : 24 April 2014
GET THIS BOOKIntroduction to Numerical Methods for Time Dependent Differential Equations

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

Finite Difference Methods for Ordinary and Partial Differential Equations

Finite Difference Methods for Ordinary and Partial Differential Equations
  • Author : Randall J. LeVeque
  • Publisher : SIAM
  • Release : 01 January 2007
GET THIS BOOKFinite Difference Methods for Ordinary and Partial Differential Equations

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.

Linear Partial Differential Equations for Scientists and Engineers

Linear Partial Differential Equations for Scientists and Engineers
  • Author : Tyn Myint-U,Lokenath Debnath
  • Publisher : Springer Science & Business Media
  • Release : 05 April 2007
GET THIS BOOKLinear Partial Differential Equations for Scientists and Engineers

This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas

Numerical Analysis of Partial Differential Equations

Numerical Analysis of Partial Differential Equations
  • Author : S. H, Lui
  • Publisher : John Wiley & Sons
  • Release : 10 January 2012
GET THIS BOOKNumerical Analysis of Partial Differential Equations

A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the

Time-dependent Partial Differential Equations and Their Numerical Solution

Time-dependent Partial Differential Equations and Their Numerical Solution
  • Author : Heinz-Otto Kreiss,Hedwig Ulmer Busenhart
  • Publisher : Birkhäuser
  • Release : 06 December 2012
GET THIS BOOKTime-dependent Partial Differential Equations and Their Numerical Solution

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.

Numerical Methods for Evolutionary Differential Equations

Numerical Methods for Evolutionary Differential Equations
  • Author : Uri M. Ascher
  • Publisher : SIAM
  • Release : 21 June 2021
GET THIS BOOKNumerical Methods for Evolutionary Differential Equations

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,

Partial Differential Equations and the Finite Element Method

Partial Differential Equations and the Finite Element Method
  • Author : Pavel Ŝolín
  • Publisher : John Wiley & Sons
  • Release : 16 December 2005
GET THIS BOOKPartial Differential Equations and the Finite Element Method

A systematic introduction to partial differential equations and modern finite element methods for their efficientnumerical solution Partial Differential Equations and the Finite Element Methodprovides a much-needed, clear, and systematic introduction tomodern theory of partial differential equations (PDEs) and finiteelement methods (FEM). Both nodal and hierachic concepts of the FEMare examined. Reflecting the growing complexity and multiscalenature of current engineering and scientific problems, the authoremphasizes higher-order finite element methods such as the spectralor hp-FEM. A solid introduction to the theory of

Numerical Solution of Partial Differential Equations by the Finite Element Method

Numerical Solution of Partial Differential Equations by the Finite Element Method
  • Author : Claes Johnson
  • Publisher : Courier Corporation
  • Release : 23 May 2012
GET THIS BOOKNumerical Solution of Partial Differential Equations by the Finite Element Method

An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods