New Sinc Methods Of Numerical Analysis

Author : Gerd Baumann
Publisher : Springer Nature
Page : 411 pages
File Size : 53,8 Mb
Release : 2021-04-23
Category : Mathematics
ISBN : 9783030497163

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New Sinc Methods of Numerical Analysis by Gerd Baumann Pdf

This contributed volume honors the 80th birthday of Frank Stenger who established new Sinc methods in numerical analysis.The contributions, written independently from each other, show the new developments in numerical analysis in connection with Sinc methods and approximations of solutions for differential equations, boundary value problems, integral equations, integrals, linear transforms, eigenvalue problems, polynomial approximations, computations on polyhedra, and many applications. The approximation methods are exponentially converging compared with standard methods and save resources in computation. They are applicable in many fields of science including mathematics, physics, and engineering.The ideas discussed serve as a starting point in many different directions in numerical analysis research and applications which will lead to new and unprecedented results. This book will appeal to a wide readership, from students to specialized experts.

Author : Frank Stenger
Publisher : CRC Press
Page : 482 pages
File Size : 40,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781439821596

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Handbook of Sinc Numerical Methods by Frank Stenger Pdf

Handbook of Sinc Numerical Methods presents an ideal road map for handling general numeric problems. Reflecting the author's advances with Sinc since 1995, the text most notably provides a detailed exposition of the Sinc separation of variables method for numerically solving the full range of partial differential equations (PDEs) of interest to sci

Author : John Lund,Kenneth L. Bowers
Publisher : SIAM
Page : 307 pages
File Size : 53,7 Mb
Release : 1992-01-01
Category : Mathematics
ISBN : 1611971632

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Sinc Methods for Quadrature and Differential Equations by John Lund,Kenneth L. Bowers Pdf

Here is an elementary development of the Sinc-Galerkin method with the focal point being ordinary and partial differential equations. This is the first book to explain this powerful computational method for treating differential equations. These methods are an alternative to finite difference and finite element schemes, and are especially adaptable to problems with singular solutions. The text is written to facilitate easy implementation of the theory into operating numerical code. The authors' use of differential equations as a backdrop for the presentation of the material allows them to present a number of the applications of the sinc method. Many of these applications are useful in numerical processes of interest quite independent of differential equations. Specifically, numerical interpolation and quadrature, while fundamental to the Galerkin development, are useful in their own right. The intimate connection between collocation and Galerkin for the sinc basis is exposed via sinc-interpolation. The quadrature rules define a class of numerical integration methods that complement better known techniques, which in the case of singular integrands, often require modification. The sinc methodology of the text is illustrated on such applications as initial data recovery, heat diffusion, advective-diffusive transport, and Burgers' equation, to illustrate the numerical implementation of the theory discussed. Engineers may find sinc methods a very competitive approach to the more common boundary element or finite element methods. Further, workers in the signal processing community may find this particular approach a refreshingly different view of the use of sinc functions. Sinc approximation is a relatively new numerical technique. This book provides a much needed elementary level explanation. It has been used for graduate numerical classes at Montana State University and Texas Tech University.

Author : Frank Stenger
Publisher : Springer Science & Business Media
Page : 580 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461227069

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Numerical Methods Based on Sinc and Analytic Functions by Frank Stenger Pdf

Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and engineers recognize that the Discrete Fourier Transform is one of a family of symbolic formulae called Sinc methods. Sinc methods are based upon the Sinc function, a wavelet-like function replete with identities which yield approximations to all classes of computational problems. Such problems include problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary layer problems. Written by the principle authority on the subject, this book introduces Sinc methods to the world of computation. It serves as an excellent research sourcebook as well as a textbook which uses analytic functions to derive Sinc methods for the advanced numerical analysis and applied approximation theory classrooms. Problem sections and historical notes are included.

Author : Adhemar Bultheel,Ronald Cools
Publisher : World Scientific
Page : 240 pages
File Size : 49,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9789812836267

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The Birth of Numerical Analysis by Adhemar Bultheel,Ronald Cools Pdf

The 1947 paper by John von Neumann and Herman Goldstine, OC Numerical Inverting of Matrices of High OrderOCO ( Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years. Sample Chapter(s). Chapter 1: Some pioneers of extrapolation methods (323 KB). Contents: Some Pioneers of Extrapolation Methods (C Brezinski); Very Basic Multidimensional Extrapolation Quadrature (J N Lyness); Numerical Methods for Ordinary Differential Equations: Early Days (J C Butcher); Interview with Herbert Bishop Keller (H M Osinga); A Personal Perspective on the History of the Numerical Analysis of Fredholm Integral Equations of the Second Kind (K Atkinson); Memoires on Building on General Purpose Numerical Algorithms Library (B Ford); Recent Trends in High Performance Computing (J J Dongarra et al.); Nonnegativity Constraints in Numerical Analysis (D-H Chen & R J Plemmons); On Nonlinear Optimization Since 1959 (M J D Powell); The History and Development of Numerical Analysis in Scotland: A Personal Perspective (G Alistair Watson); Remembering Philip Rabinowitz (P J Davis & A S Fraenkel); My Early Experiences with Scientific Computation (P J Davis); Applications of Chebyshev Polynomials: From Theoretical Kinematics to Practical Computations (R Piessens). Readership: Mathematicians in numerical analysis and mathematicians who are interested in the history of mathematics.

Author : Richard Paul Shaw
Publisher : Charlottesville : University Press of Virginia
Page : 840 pages
File Size : 55,7 Mb
Release : 1980
Category : Engineering mathematics
ISBN : UCAL:B4132278

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Innovative Numerical Analysis for the Engineering Sciences by Richard Paul Shaw Pdf

Author : James P Howard, II
Publisher : CRC Press
Page : 257 pages
File Size : 41,6 Mb
Release : 2017-07-12
Category : Mathematics
ISBN : 9781498723640

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Computational Methods for Numerical Analysis with R by James P Howard, II Pdf

Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.

Author : Germund Dahlquist,Ake Bjorck
Publisher : SIAM
Page : 741 pages
File Size : 42,7 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780898716443

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Numerical Methods in Scientific Computing: by Germund Dahlquist,Ake Bjorck Pdf

This work addresses the increasingly important role of numerical methods in science and engineering. It combines traditional and well-developed topics with other material such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions.

Author : R. Glowinski
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 41,8 Mb
Release : 2008-01-22
Category : Mathematics
ISBN : 9783540775065

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Lectures on Numerical Methods for Non-Linear Variational Problems by R. Glowinski Pdf

When Herb Keller suggested, more than two years ago, that we update our lectures held at the Tata Institute of Fundamental Research in 1977, and then have it published in the collection Springer Series in Computational Physics, we thought, at first, that it would be an easy task. Actually, we realized very quickly that it would be more complicated than what it seemed at first glance, for several reasons: 1. The first version of Numerical Methods for Nonlinear Variational Problems was, in fact, part of a set of monographs on numerical mat- matics published, in a short span of time, by the Tata Institute of Fun- mental Research in its well-known series Lectures on Mathematics and Physics; as might be expected, the first version systematically used the material of the above monographs, this being particularly true for Lectures on the Finite Element Method by P. G. Ciarlet and Lectures on Optimization—Theory and Algorithms by J. Cea. This second version had to be more self-contained. This necessity led to some minor additions in Chapters I-IV of the original version, and to the introduction of a chapter (namely, Chapter Y of this book) on relaxation methods, since these methods play an important role in various parts of this book.

Author : A. Cohen
Publisher : Elsevier
Page : 354 pages
File Size : 42,6 Mb
Release : 2003-04-29
Category : Mathematics
ISBN : 0080537855

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Numerical Analysis of Wavelet Methods by A. Cohen Pdf

Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and function spaces, and plays a pivotal role in the analysis of wavelet-based numerical methods. This book offers a self-contained treatment of wavelets, which includes this theoretical pillar and it applications to the numerical treatment of partial differential equations. Its key features are: 1. Self-contained introduction to wavelet bases and related numerical algorithms, from the simplest examples to the most numerically useful general constructions. 2. Full treatment of the theoretical foundations that are crucial for the analysis of wavelets and other related multiscale methods : function spaces, linear and nonlinear approximation, interpolation theory. 3. Applications of these concepts to the numerical treatment of partial differential equations : multilevel preconditioning, sparse approximations of differential and integral operators, adaptive discretization strategies.

Author : Myron B. Allen, III,Eli L. Isaacson
Publisher : John Wiley & Sons
Page : 592 pages
File Size : 49,5 Mb
Release : 2019-03-19
Category : Mathematics
ISBN : 9781119245469

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Numerical Analysis for Applied Science by Myron B. Allen, III,Eli L. Isaacson Pdf

Pragmatic and Adaptable Textbook Meets the Needs of Students and Instructors from Diverse Fields Numerical analysis is a core subject in data science and an essential tool for applied mathematicians, engineers, and physical and biological scientists. This updated and expanded edition of Numerical Analysis for Applied Science follows the tradition of its precursor by providing a modern, flexible approach to the theory and practical applications of the field. As before, the authors emphasize the motivation, construction, and practical considerations before presenting rigorous theoretical analysis. This approach allows instructors to adapt the textbook to a spectrum of uses, ranging from one-semester, methods-oriented courses to multi-semester theoretical courses. The book includes an expanded first chapter reviewing useful tools from analysis and linear algebra. Subsequent chapters include clearly structured expositions covering the motivation, practical considerations, and theory for each class of methods. The book includes over 250 problems exploring practical and theoretical questions and 32 pseudocodes to help students implement the methods. Other notable features include: A preface providing advice for instructors on using the text for a single semester course or multiple-semester sequence of courses Discussion of topics covered infrequently by other texts at this level, such as multidimensional interpolation, quasi-Newton methods in several variables, multigrid methods, preconditioned conjugate-gradient methods, finite-difference methods for partial differential equations, and an introduction to finite-element theory New topics and expanded treatment of existing topics to address developments in the field since publication of the first edition More than twice as many computational and theoretical exercises as the first edition. Numerical Analysis for Applied Science, Second Edition provides an excellent foundation for graduate and advanced undergraduate courses in numerical methods and numerical analysis. It is also an accessible introduction to the subject for students pursuing independent study in applied mathematics, engineering, and the physical and life sciences and a valuable reference for professionals in these areas.

Author : Brian Sutton
Publisher : SIAM
Page : 448 pages
File Size : 52,5 Mb
Release : 2019-04-18
Category : Mathematics
ISBN : 9781611975697

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Numerical Analysis by Brian Sutton Pdf

This textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems?interpolation, integration, linear systems, zero finding, and differential equations?are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones; a dual emphasis on theory and experimentation; the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects; and many examples and exercises. Numerical Analysis: Theory and Experiments is designed to be the primary text for a junior- or senior-level undergraduate course in numerical analysis for mathematics majors. Scientists and engineers interested in numerical methods, particularly those seeking an accessible introduction to Chebyshev methods, will also be interested in this book.

Author : William F. Ames
Publisher : Academic Press
Page : 451 pages
File Size : 50,6 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080571300

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Numerical Methods for Partial Differential Equations by William F. Ames Pdf

This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation. Material on finite elements and finite differences have been merged, and now constitute equal partners Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods References have been updated, and reflect the additional material Self-contained nature of the Second Edition has been maintained Very suitable for PDE courses

Author : Frank Stenger,Don Tucker,Gerd Baumann
Publisher : Springer
Page : 226 pages
File Size : 52,8 Mb
Release : 2016-09-23
Category : Mathematics
ISBN : 9783319275260

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Navier–Stokes Equations on R3 × [0, T] by Frank Stenger,Don Tucker,Gerd Baumann Pdf

In this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier–Stokes partial differential equations on (x, y, z, t) ∈ R3 × [0, T]. Initially converting the PDE to a system of integral equations, the authors then describe spaces A of analytic functions that house solutions of this equation, and show that these spaces of analytic functions are dense in the spaces S of rapidly decreasing and infinitely differentiable functions. This method benefits from the following advantages: The functions of S are nearly always conceptual rather than explicit Initial and boundary conditions of solutions of PDE are usually drawn from the applied sciences, and as such, they are nearly always piece-wise analytic, and in this case, the solutions have the same properties When methods of approximation are applied to functions of A they converge at an exponential rate, whereas methods of approximation applied to the functions of S converge only at a polynomial rate Enables sharper bounds on the solution enabling easier existence proofs, and a more accurate and more efficient method of solution, including accurate error bounds Following the proofs of denseness, the authors prove the existence of a solution of the integral equations in the space of functions A ∩ R3 × [0, T], and provide an explicit novel algorithm based on Sinc approximation and Picard–like iteration for computing the solution. Additionally, the authors include appendices that provide a custom Mathematica program for computing solutions based on the explicit algorithmic approximation procedure, and which supply explicit illustrations of these computed solutions.

Author : Hans-Görg Roos,Martin Stynes,Lutz Tobiska
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 45,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662032060

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Numerical Methods for Singularly Perturbed Differential Equations by Hans-Görg Roos,Martin Stynes,Lutz Tobiska Pdf

The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.