Introduction To Numerical Methods
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Introduction To Numerical Methods In Differential Equations
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Author : Mark H. Holmes
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-05
Introduction To Numerical Methods In Differential Equations written by Mark H. Holmes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-05 with Mathematics categories.
The title gives a reasonable ?rst-order approximation to what this book is about. To explain why, let’s start with the expression “di?erential equations.” These are essential in science and engineering, because the laws of nature t- ically result in equations relating spatial and temporal changes in one or more variables.Todevelopanunderstandingofwhatisinvolvedin?ndingsolutions, the book begins with problems involving derivatives for only one independent variable, and these give rise to ordinary di?erential equations. Speci?cally, the ?rst chapter considers initial value problems (time derivatives), and the second concentrates on boundary value problems (space derivatives). In the succeeding four chapters problems involving both time and space derivatives, partial di?erential equations, are investigated. This brings us to the next expression in the title: “numerical methods.” This is a book about how to transform differential equations into problems that can be solved using a computer.The fact is that computers are only able to solve discrete problems and generally do this using ?nite-precision arithmetic. What this means is that in deriving and then using a numerical algorithmthecorrectnessofthediscreteapproximationmustbeconsidered,as must the consequences of round-o? error in using ?oating-point arithmetic to calculatetheanswer.Oneoftheinterestingaspectsofthesubjectisthatwhat appears to be an obviously correct numerical method can result in complete failure. Consequently, although the book concentrates on the derivation and use of numerical methods, the theoretical underpinnings are also presented andusedinthedevelopment.
Introduction To Numerical Analysis
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Author : J. Stoer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Introduction To Numerical Analysis written by J. Stoer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.
Numerical Continuation Methods
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Author : Eugene L. Allgower
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Continuation Methods written by Eugene L. Allgower and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.
Computational Engineering Introduction To Numerical Methods
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Author : Michael Schäfer
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-20
Computational Engineering Introduction To Numerical Methods written by Michael Schäfer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-20 with Mathematics categories.
Introduction.- Modelling of Continuum Mechanical Problems.- Discretization of Problem Domain.- Finite-Volume Methods.- Finite-Element Methods.- Time Discretization.- Solution of Algebraic Systems of Equations.- Properties of Numerical Methods.- Finite-Element Methods in Structural Mechanics.- Finite-Volume Methods for Incompressible Flows.- Acceleration of Computations.- List of Symbols.- References.- Index.
Introduction To Numerical Methods
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Author : Peter Stark
language : en
Publisher: Simon & Schuster Books For Young Readers
Release Date : 1970
Introduction To Numerical Methods written by Peter Stark and has been published by Simon & Schuster Books For Young Readers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
This text is for an introductory course in what is commonly called numerical analysis, numerical methods, or even numerical calculus. While it parallels the development in Course B4 on Numerical Calculus in the proposed Curriculum in Computer Science issued by the Association for Computing Machinery, this book is designed for any science or engineering student who has completed his first course in calculus, and who has at least a passing knowledge of elementary computer programming in FORTRAN. This is a practical book for the student who, in addition to seeing the theory of numerical methods, also likes to see the results; the predominant emphasis is on specific methods and computer solutions. It often points out where the theory departs from practice, and it illustrates each method of computer solution by an actual computer program and its results.
A Concise Introduction To Numerical Analysis
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Author : A. C. Faul
language : en
Publisher: CRC Press
Release Date : 2016-03-23
A Concise Introduction To Numerical Analysis written by A. C. Faul and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-23 with Mathematics categories.
This textbook provides an accessible and concise introduction to numerical analysis for upper undergraduate and beginning graduate students from various backgrounds. It was developed from the lecture notes of four successful courses on numerical analysis taught within the MPhil of Scientific Computing at the University of Cambridge. The book is easily accessible, even to those with limited knowledge of mathematics. Students will get a concise, but thorough introduction to numerical analysis. In addition the algorithmic principles are emphasized to encourage a deeper understanding of why an algorithm is suitable, and sometimes unsuitable, for a particular problem. A Concise Introduction to Numerical Analysis strikes a balance between being mathematically comprehensive, but not overwhelming with mathematical detail. In some places where further detail was felt to be out of scope of the book, the reader is referred to further reading. The book uses MATLAB® implementations to demonstrate the workings of the method and thus MATLAB's own implementations are avoided, unless they are used as building blocks of an algorithm. In some cases the listings are printed in the book, but all are available online on the book’s page at www.crcpress.com. Most implementations are in the form of functions returning the outcome of the algorithm. Also, examples for the use of the functions are given. Exercises are included in line with the text where appropriate, and each chapter ends with a selection of revision exercises. Solutions to odd-numbered exercises are also provided on the book’s page at www.crcpress.com. This textbook is also an ideal resource for graduate students coming from other subjects who will use numerical techniques extensively in their graduate studies.
An Introduction To Numerical Analysis
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Author : Kendall Atkinson
language : en
Publisher: John Wiley & Sons
Release Date : 1991-01-16
An Introduction To Numerical Analysis written by Kendall Atkinson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-16 with Mathematics categories.
This Second Edition of a standard numerical analysis text retains organization of the original edition, but all sections have been revised, some extensively, and bibliographies have been updated. New topics covered include optimization, trigonometric interpolation and the fast Fourier transform, numerical differentiation, the method of lines, boundary value problems, the conjugate gradient method, and the least squares solutions of systems of linear equations. Contains many problems, some with solutions.
A Theoretical Introduction To Numerical Analysis
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Author : Victor S. Ryaben'kii
language : en
Publisher: CRC Press
Release Date : 2006-11-02
A Theoretical Introduction To Numerical Analysis written by Victor S. Ryaben'kii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-02 with Mathematics categories.
A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An accessible yet rigorous mathematical introduction, this book provides a pedagogical account of the fundamentals of numerical analysis. The authors thoroughly explain basic concepts, such as discretization, error, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the effect of smoothness on the accuracy of approximation in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. Another advanced subject discussed, the method of difference potentials, employs discrete analogues of Calderon’s potentials and boundary projection operators. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation. By lucidly presenting the central mathematical concepts of numerical methods, A Theoretical Introduction to Numerical Analysis provides a foundational link to more specialized computational work in fluid dynamics, acoustics, and electromagnetism.
Introduction To Numerical Analysis
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Author : Alastair Wood
language : en
Publisher: Addison Wesley Longman
Release Date : 1999
Introduction To Numerical Analysis written by Alastair Wood and has been published by Addison Wesley Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
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Python Programming And Numerical Methods
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Author : Qingkai Kong
language : en
Publisher: Academic Press
Release Date : 2020-12-02
Python Programming And Numerical Methods written by Qingkai Kong and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-02 with Technology & Engineering categories.
Python Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the goal of helping the students to develop good computational problem-solving techniques through the use of numerical methods and the Python programming language. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level that allows students to quickly apply results in practical settings.