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Introduction to Numerical Methods for Variational Problems

2019-09-26 Mathematics
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Release : 2019-09-26
Genre : Mathematics
Kind : eBook
Book Rating : 885/5 ( reviews)

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Book Synopsis Introduction to Numerical Methods for Variational Problems by : Hans Petter Langtangen

Download or read book Introduction to Numerical Methods for Variational Problems written by Hans Petter Langtangen. This book was released on 2019-09-26. Available in PDF, EPUB and Kindle. Book excerpt: This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

Numerical Methods for Partial Differential Equations

2016-04-28 Technology & Engineering
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Release : 2016-04-28
Genre : Technology & Engineering
Kind : eBook
Book Rating : 366/5 ( reviews)

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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. This book was released on 2016-04-28. 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.

Introduction to Numerical Analysis

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 729/5 ( reviews)

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Book Synopsis Introduction to Numerical Analysis by : J. Stoer

Download or read book Introduction to Numerical Analysis written by J. Stoer. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: 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 Methods for Nonlinear Variational Problems

1984 Numerical analysis
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Release : 1984
Genre : Numerical analysis
Kind : eBook
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Book Synopsis Numerical Methods for Nonlinear Variational Problems by : R. Glowinski

Download or read book Numerical Methods for Nonlinear Variational Problems written by R. Glowinski. This book was released on 1984. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Numerical Methods for Non-Linear Variational Problems

2008-01-22 Mathematics
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Release : 2008-01-22
Genre : Mathematics
Kind : eBook
Book Rating : 064/5 ( reviews)

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Book Synopsis Lectures on Numerical Methods for Non-Linear Variational Problems by : R. Glowinski

Download or read book Lectures on Numerical Methods for Non-Linear Variational Problems written by R. Glowinski. This book was released on 2008-01-22. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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