Download or read book Accuracy Study of Finite Difference Methods written by Nancy Jane Cyrus and published by . This book was released on 1968 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Accuracy Study of Finite Difference Methods written by Nancy Jane Cyrus and published by . This book was released on 1968 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book An Accuracy Study of Central Finite Difference Methods in Second Order Boundary Value Problems written by Nancy Jane Cyrus and published by . This book was released on 1966 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Analysis of Finite Difference Schemes written by Boško S. Jovanović and published by Springer Science & Business Media. This book was released on 2013-10-22 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Finite Difference Schemes and Partial Differential Equations written by John C. Strikwerda and published by Springer. This book was released on 1989-09-28 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Operational Unification of Finite Difference Methods for the Numerical Integration of Ordinary Differential Equations written by Harvard Lomax and published by . This book was released on 1967 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: One purpose of this report is to present a mathematical procedure which can be used to study and compare various numerical methods for integrating ordinary differential equations. This procedure is relatively simple, mathematically rigorous, and of such a nature that matters of interest in digital computations, such as machine memory and running time, can be weighed against the accuracy and stability provided by the method under consideration. Briefly, the procedure is as follows: (1) Find a single differential equation that is sufficiently representative (this is fully defined in the report) of an arbitrary number of nonhomogeneous, linear, ordinary differential equations with constant coefficients. (2) Solve this differential equation exactly. (3) Choose any given numerical method, use it -- in its entirety -- to reduce the differential equation to difference equations, and, by means of operational techniques, solve the latter exactly. (4) Study and compare the results of (2) and (3). Conceptually there is nothing new in this procedure, but the particular development presented in this report does not appear to have been carried out before. Another purpose is to use the procedure just described to analyze a variety of numerical methods, ranging from classical, predictor-corrector systems to Runge-Kutta techniques and including various combinations of the two.

Download or read book Introductory Finite Difference Methods for PDEs written by and published by Bookboon. This book was released on with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Accuracy of Finite Element Approximations to Structural Problems written by Langley Research Center and published by . This book was released on 1970 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Solution of Partial Differential Equations by Finite Difference Approximations written by Lewis Hall Msc and published by Independently Published. This book was released on 2018-09-14 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Accuracy of Finite Difference Methods in Recirculating Flows written by R. A. Beier and published by . This book was released on 1982 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Finite Difference Modelling of Earthquake Motions written by Peter Moczo and published by Cambridge University Press. This book was released on 2014-04-24 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate students in earthquake seismology, computational and numerical modelling, and applied mathematics.

Download or read book Finite Difference Methods in Financial Engineering written by Daniel J. Duffy and published by John Wiley & Sons. This book was released on 2013-10-28 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.

Download or read book Finite Difference Methods Theory and Applications written by Ivan Dimov and published by Springer. This book was released on 2015-06-16 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Finite Difference Methods, FDM 2014, held in Lozenetz, Bulgaria, in June 2014. The 36 revised full papers were carefully reviewed and selected from 62 submissions. These papers together with 12 invited papers cover topics such as finite difference and combined finite difference methods as well as finite element methods and their various applications in physics, chemistry, biology and finance.

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.

Download or read book Finite Difference Computing with PDEs written by Hans Petter Langtangen and published by Springer. This book was released on 2017-06-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.