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Numerical Approximation Methods

2011-09-28 Mathematics
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Release : 2011-09-28
Genre : Mathematics
Kind : eBook
Book Rating : 365/5 ( reviews)

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Book Synopsis Numerical Approximation Methods by : Harold Cohen

Download or read book Numerical Approximation Methods written by Harold Cohen. This book was released on 2011-09-28. Available in PDF, EPUB and Kindle. Book excerpt: This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.

Numerical Approximation Methods for Elliptic Boundary Value Problems

2007-12-22 Mathematics
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Release : 2007-12-22
Genre : Mathematics
Kind : eBook
Book Rating : 056/5 ( reviews)

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Book Synopsis Numerical Approximation Methods for Elliptic Boundary Value Problems by : Olaf Steinbach

Download or read book Numerical Approximation Methods for Elliptic Boundary Value Problems written by Olaf Steinbach. This book was released on 2007-12-22. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.

Numerical Approximation of Partial Differential Equations

2009-02-11 Mathematics
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Release : 2009-02-11
Genre : Mathematics
Kind : eBook
Book Rating : 689/5 ( reviews)

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Book Synopsis Numerical Approximation of Partial Differential Equations by : Alfio Quarteroni

Download or read book Numerical Approximation of Partial Differential Equations written by Alfio Quarteroni. This book was released on 2009-02-11. Available in PDF, EPUB and Kindle. Book excerpt: Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).

Numerical Approximation of Partial Differential Equations

2016-06-02 Mathematics
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Release : 2016-06-02
Genre : Mathematics
Kind : eBook
Book Rating : 547/5 ( reviews)

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Book Synopsis Numerical Approximation of Partial Differential Equations by : Sören Bartels

Download or read book Numerical Approximation of Partial Differential Equations written by Sören Bartels. This book was released on 2016-06-02. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.

An Introduction to Numerical Methods and Analysis

2013-06-06 Mathematics
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Release : 2013-06-06
Genre : Mathematics
Kind : eBook
Book Rating : 230/5 ( reviews)

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Book Synopsis An Introduction to Numerical Methods and Analysis by : James F. Epperson

Download or read book An Introduction to Numerical Methods and Analysis written by James F. Epperson. This book was released on 2013-06-06. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." —Zentrablatt Math ". . . carefully structured with many detailed worked examples . . ." —The Mathematical Gazette ". . . an up-to-date and user-friendly account . . ." —Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics. A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth. The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.

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