Finite Difference Approximations to Solutions of Partial Differential Equations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Finite Difference Approximations to Solutions of Partial Differential Equations PDF full book. Access full book title Finite Difference Approximations to Solutions of Partial Differential Equations by Burton Wendroff. Download full books in PDF and EPUB format.
Author: Burton Wendroff
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 68
Get Book
Book Description
Author: Burton Wendroff
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 68
Get Book
Book Description
Author: Boško S. Jovanović
Publisher: Springer Science & Business Media
ISBN: 1447154606
Category : Mathematics
Languages : en
Pages : 408
Get Book
Book Description
This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.
Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
Get Book
Book Description
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: SUJAUL CHOWDHURY
Publisher: American Academic Press
ISBN: 1631819933
Category : Mathematics
Languages : en
Pages : 94
Get Book
Book Description
The book is intended for graduate students of Engineering, Mathematics and Physics. We have numerically solved Hyperbolic and Parabolic partial differential equations with various initial conditions using Finite Difference Method and Mathematica. Replacing derivatives by finite difference approximations in these differential equations in conjunction with boundary conditions and initial conditions lead to equations relating numerical solutions at various position and time. These relations are intricate in that numerical value of the solution at one particular position and time is related with that at several other position and time. We have surmounted the intricacies by writing programs in Mathematica 6.0 that neatly provide systematic tabulation of the numerical values for all necessary position and time. This enabled us to plot the solutions as functions of position and time. Comparison with analytic solutions revealed nearly perfect match in every case. We have demonstrated conditions under which the nearly perfect match can be obtained even for larger increments in position or time.
Author: J.W. Thomas
Publisher: Springer Science & Business Media
ISBN: 1489972781
Category : Mathematics
Languages : en
Pages : 451
Get Book
Book Description
What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.
Author: Lewis Hall Msc
Publisher: Independently Published
ISBN: 9781720010432
Category : Mathematics
Languages : en
Pages : 110
Get Book
Book Description
A comprehensive performance analysis of the Finite Difference Method for the solution of Partial Differential Equations. Providing an in-depth understanding of; Finite Difference Methods, their applications, theoretical basis, the full derivation of Taylor Series Expansions and the construction of a working Computational Domain Grid System. Furthermore, detailing and showing how to effectively employ the Finite Difference Method, through the implementation of Finite Difference Schemes, to obtain accurate, stable and consistent numerical solutions for Partial Differential Equations, which model a multitude of varying dynamic processes. Moreover, it contains a detailed, thorough performance analysis investigation of three different Finite Difference Method schemes, when they are employed to obtain accurate numerical solutions for a fluid flow heat transfer process that is modelled by a first order Partial Differential Equation. These three schemes are the Forward-Time-Backwards-Space, Lax and Lax Wendroff Finite Difference Method schemes. Additionally, it explains the criteria that is required for optimal scheme stability, consistency and convergence. A brief breakdown of what the book contains;* A Description of the processes required to conduct an effective performance analysis of Finite Difference Method Schemes. * It specifies and explains the Forward-Time-Backwards-Space, Lax and Lax-Wendroff Finite Difference Scheme equations.* Explanations of the concepts of Finite Difference Method Stability, Consistency and Convergence. * The full derivations of the Taylor Series Expansions of the Forward-Time-Backwards-Space, Lax and Lax-Wendroff Finite Difference Scheme equations.* The development of an effective Finite Difference Method Computational Grid System, that can be used to calculate accurate numerical solutions for Partial Differential Equations. * A comprehensive end-to-end performance analysis of the three schemes for a fluid flow heat transfer process.* A discussion of the usefulness of the Finite Difference Method for solving Partial Differential Equations.* An overview of how to select an optimal Finite Difference Method scheme for accurate numerical solutions.You will gain valuable knowledge of the Finite Difference Method and its applications, expanding your expertise and intellect in this area of mathematics. Additionally, it will enable you to develop a systematic understanding of how to use Finite Difference Schemes to solve Partial Differential Equations and obtain accurate numerical solutions for dynamic processes. The book is self-contained allowing you to understand and conduct a Finite Difference Method performance analysis, so that you can apply the concepts to any process that is modelled by hyperbolic Partial Differential Equations. Furthermore, it is particularly valuable to; academics, educators, scholars, engineering industry professionals, and students. Especially, postgraduate Master's and undergraduate students. Assisting those who work/operate/study in the fields of Aerodynamics, Mathematics, Aerospace, Fluid Dynamics and Fluid Mechanics. Overall, this book will save you countless hours of research and reading, since the information contained within is distilled, concentrated and assimilated in an effective manner to help you to develop a deep understanding regarding the performance of the Finite Difference Method.
Author: A. R. Mitchell
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 296
Get Book
Book Description
Extensively revised edition of Computational Methods in Partial Differential Equations. A more general approach has been adopted for the splitting of operators for parabolic and hyperbolic equations to include Richtmyer and Strang type splittings in addition to alternating direction implicit and locally one dimensional methods. A description of the now standard factorization and SOR/ADI iterative techniques for solving elliptic difference equations has been supplemented with an account or preconditioned conjugate gradient methods which are currently gaining in popularity. Prominence is also given to the Galerkin method using different test and trial functions as a means of constructing difference approximations to both elliptic and time dependent problems. The applications of finite difference methods have been revised and contain examples involving the treatment of singularities in elliptic equations, free and moving boundary problems, as well as modern developments in computational fluid dynamics. Emphasis throughout is on clear exposition of the construction and solution of difference equations. Material is reinforced with theoretical results when appropriate.
Author: Bertil Gustafsson
Publisher: John Wiley & Sons
ISBN: 1118548523
Category : Mathematics
Languages : en
Pages : 464
Get Book
Book Description
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: David F. Griffiths
Publisher: Springer
ISBN: 3319225693
Category : Mathematics
Languages : en
Pages : 368
Get Book
Book Description
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.
Author:
Publisher: Bookboon
ISBN: 8776816427
Category :
Languages : en
Pages : 144
Get Book
Book Description
