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Time Dependent Partial Differential Equations And Their Numerical Solution
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Book Synopsis Time-dependent Partial Differential Equations and Their Numerical Solution by : Heinz-Otto Kreiss
Download or read book Time-dependent Partial Differential Equations and Their Numerical Solution written by Heinz-Otto Kreiss and published by Birkhäuser. This book was released on 2012-12-06 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Numerical Methods for Time Dependent Differential Equations by : Heinz-Otto Kreiss
Download or read book Introduction to Numerical Methods for Time Dependent Differential Equations written by Heinz-Otto Kreiss and published by John Wiley & Sons. This book was released on 2014-04-24 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers by : Moysey Brio
Download or read book Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers written by Moysey Brio and published by Academic Press. This book was released on 2010-09-21 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Finite Difference Methods for Ordinary and Partial Differential Equations by : Randall J. LeVeque
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis High Order Difference Methods for Time Dependent PDE by : Bertil Gustafsson
Download or read book High Order Difference Methods for Time Dependent PDE written by Bertil Gustafsson and published by Springer Science & Business Media. This book was released on 2007-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by : Willem Hundsdorfer
Download or read book Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations written by Willem Hundsdorfer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unique book on Reaction-Advection-Diffusion problems
Book Synopsis Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition) by : Granville Sewell
Download or read book Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition) written by Granville Sewell and published by World Scientific. This book was released on 2014-12-16 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A.The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions.The Windows version of PDE2D comes free with every purchase of this book. More information at www.pde2d.com/contact.
Book Synopsis Time-Dependent Problems and Difference Methods by : Bertil Gustafsson
Download or read book Time-Dependent Problems and Difference Methods written by Bertil Gustafsson and published by John Wiley & Sons. This book was released on 2013-07-18 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Partial Differential Equations with Numerical Methods by : Stig Larsson
Download or read book Partial Differential Equations with Numerical Methods written by Stig Larsson and published by Springer Science & Business Media. This book was released on 2008-12-05 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.
Book Synopsis Numerical Methods for Evolutionary Differential Equations by : Uri M. Ascher
Download or read book Numerical Methods for Evolutionary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 2008-01-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Methods for Partial Differential Equations by : Vitoriano Ruas
Download or read book Numerical Methods for Partial Differential Equations written by Vitoriano Ruas and published by John Wiley & Sons. This book was released on 2016-04-28 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.
Book Synopsis Time Dependent Problems and Difference Methods by : Bertil Gustafsson
Download or read book Time Dependent Problems and Difference Methods written by Bertil Gustafsson and published by John Wiley & Sons. This book was released on 1995 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Book Synopsis The Numerical Solution of Ordinary and Partial Differential Equations by : Granville Sewell
Download or read book The Numerical Solution of Ordinary and Partial Differential Equations written by Granville Sewell and published by John Wiley & Sons. This book was released on 2005-07-25 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn to write programs to solve ordinary and partial differential equations The Second Edition of this popular text provides an insightful introduction to the use of finite difference and finite element methods for the computational solution of ordinary and partial differential equations. Readers gain a thorough understanding of the theory underlying themethods presented in the text. The author emphasizes the practical steps involved in implementing the methods, culminating in readers learning how to write programs using FORTRAN90 and MATLAB(r) to solve ordinary and partial differential equations. The book begins with a review of direct methods for the solution of linear systems, with an emphasis on the special features of the linear systems that arise when differential equations are solved. The following four chapters introduce and analyze the more commonly used finite difference methods for solving a variety of problems, including ordinary and partial differential equations and initial value and boundary value problems. The techniques presented in these chapters, with the aid of carefully developed exercises and numerical examples, can be easilymastered by readers. The final chapter of the text presents the basic theory underlying the finite element method. Following the guidance offered in this chapter, readers gain a solid understanding of the method and discover how to use it to solve many problems. A special feature of the Second Edition is Appendix A, which describes a finite element program, PDE2D, developed by the author. Readers discover how PDE2D can be used to solve difficult partial differential equation problems, including nonlinear time-dependent and steady-state systems, and linear eigenvalue systems in 1D intervals, general 2D regions, and a wide range of simple 3D regions. The software itself is available to instructors who adopt the text to share with their students.
Book Synopsis Some Recent Methods for the Numerical Solution of Time Dependent Partial Differential Equations by : A. R. Gourlay
Download or read book Some Recent Methods for the Numerical Solution of Time Dependent Partial Differential Equations written by A. R. Gourlay and published by . This book was released on 1970 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of Partial Differential Equations by the Finite Element Method by : Claes Johnson
Download or read book Numerical Solution of Partial Differential Equations by the Finite Element Method written by Claes Johnson and published by Courier Corporation. This book was released on 2012-05-23 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
Book Synopsis Numerical Methods for Solving Time-dependent Problems for Partial Differential Equations by : Heinz-Otto Kreiss
Download or read book Numerical Methods for Solving Time-dependent Problems for Partial Differential Equations written by Heinz-Otto Kreiss and published by . This book was released on 1978 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Some Recent Methods for the Numerical Solution of Time Dependent Partial Differential Equations by :
Download or read book Some Recent Methods for the Numerical Solution of Time Dependent Partial Differential Equations written by and published by . This book was released on 1970 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
