Numerical Approximation Methods

Author : Harold Cohen
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 42,9 Mb
Release : 2011-09-28
Category : Mathematics
ISBN : 9781441998361

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Numerical Approximation Methods by Harold Cohen Pdf

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.

Author : Olaf Steinbach
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 43,8 Mb
Release : 2007-12-22
Category : Mathematics
ISBN : 9780387688053

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Numerical Approximation Methods for Elliptic Boundary Value Problems by Olaf Steinbach Pdf

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.

Author : Alfio Quarteroni,Alberto Valli
Publisher : Springer Science & Business Media
Page : 551 pages
File Size : 52,9 Mb
Release : 2009-02-11
Category : Mathematics
ISBN : 9783540852681

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Numerical Approximation of Partial Differential Equations by Alfio Quarteroni,Alberto Valli Pdf

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).

Author : Sören Bartels
Publisher : Springer
Page : 535 pages
File Size : 49,7 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9783319323541

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Numerical Approximation of Partial Differential Equations by Sören Bartels Pdf

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.

Author : James F. Epperson
Publisher : John Wiley & Sons
Page : 579 pages
File Size : 42,5 Mb
Release : 2013-06-06
Category : Mathematics
ISBN : 9781118626238

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An Introduction to Numerical Methods and Analysis by James F. Epperson Pdf

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.

Author : Hervé Le Dret,Brigitte Lucquin
Publisher : Birkhäuser
Page : 395 pages
File Size : 46,7 Mb
Release : 2016-02-11
Category : Mathematics
ISBN : 9783319270678

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Partial Differential Equations: Modeling, Analysis and Numerical Approximation by Hervé Le Dret,Brigitte Lucquin Pdf

This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.

Author : Jukka Saranen,Gennadi Vainikko
Publisher : Springer Science & Business Media
Page : 461 pages
File Size : 52,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662047965

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Periodic Integral and Pseudodifferential Equations with Numerical Approximation by Jukka Saranen,Gennadi Vainikko Pdf

An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.

Author : Hans-Jürgen Reinhardt
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210801

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Analysis of Approximation Methods for Differential and Integral Equations by Hans-Jürgen Reinhardt Pdf

This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite difference methods and of projection methods for approximating their variational formulations.

Author : B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor
Publisher : Springer
Page : 446 pages
File Size : 53,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540498049

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Advanced Numerical Approximation of Nonlinear Hyperbolic Equations by B. Cockburn,C. Johnson,C.-W. Shu,E. Tadmor Pdf

This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.

Author : Justin Solomon
Publisher : CRC Press
Page : 400 pages
File Size : 43,9 Mb
Release : 2015-06-24
Category : Computers
ISBN : 9781482251890

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Numerical Algorithms by Justin Solomon Pdf

Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

Author : Karan S. Surana
Publisher : CRC Press
Page : 256 pages
File Size : 51,7 Mb
Release : 2018-10-31
Category : Mathematics
ISBN : 9780429647864

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Numerical Methods and Methods of Approximation in Science and Engineering by Karan S. Surana Pdf

Numerical Methods and Methods of Approximation in Science and Engineering prepares students and other readers for advanced studies involving applied numerical and computational analysis. Focused on building a sound theoretical foundation, it uses a clear and simple approach backed by numerous worked examples to facilitate understanding of numerical methods and their application. Readers will learn to structure a sequence of operations into a program, using the programming language of their choice; this approach leads to a deeper understanding of the methods and their limitations. Features: Provides a strong theoretical foundation for learning and applying numerical methods Takes a generic approach to engineering analysis, rather than using a specific programming language Built around a consistent, understandable model for conducting engineering analysis Prepares students for advanced coursework, and use of tools such as FEA and CFD Presents numerous detailed examples and problems, and a Solutions Manual for instructors

Author : Edwige Godlewski,Pierre-Arnaud Raviart
Publisher : Springer Nature
Page : 846 pages
File Size : 47,9 Mb
Release : 2021-08-28
Category : Mathematics
ISBN : 9781071613443

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Numerical Approximation of Hyperbolic Systems of Conservation Laws by Edwige Godlewski,Pierre-Arnaud Raviart Pdf

This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.

Author : G. A. Watson
Publisher : John Wiley & Sons
Page : 248 pages
File Size : 46,8 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39015015733853

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Approximation Theory and Numerical Methods by G. A. Watson Pdf

Author : James P Howard, II
Publisher : CRC Press
Page : 257 pages
File Size : 49,6 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 : Kenneth L. Judd
Publisher : MIT Press
Page : 657 pages
File Size : 48,8 Mb
Release : 2023-04-04
Category : Business & Economics
ISBN : 9780262547741

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Numerical Methods in Economics by Kenneth L. Judd Pdf

To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A website contains supplementary material including programs and answers to exercises.