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Weighted Residual Methods

Weighted Residual Methods Book
Author : Mohammad Hatami
Publisher : Academic Press
Release : 2017-11-07
ISBN : 0128132191
Language : En, Es, Fr & De

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Book Description :

Weighted Residual Methods: Principles, Modifications and Applications introduces a range of WRMs, providing examples that show how they can be used to solve complex engineering problems with greater accuracy and computational efficiency. Examples focus on non-linear problems, including the motion of a spherical particle, nanofluid flow and heat transfer, magnetohydrodynamic flow and heat transfer, and micropolar fluid flow and heat transfer. These are important factors in understanding processes, such as filtration, combustion, air and water pollution and micro contamination. In addition to the applications, the reader is provided with full derivations of equations and summaries of important field research. Includes the basic code for each method, giving readers a head start in using WRMs for computational modeling Provides full derivations of important governing equations in a number of emerging fields of study Offers numerous, detailed examples of a range of applications in heat transfer, nanotechnology, medicine, and more

Investigation of the Numerical Methods of Finite Differences and Weighted Residuals for Solution of the Heat Equation

Investigation of the Numerical Methods of Finite Differences and Weighted Residuals for Solution of the Heat Equation Book
Author : Robert Earl Naegeli,AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING.
Publisher : Unknown
Release : 1982
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The method of weighted residuals applied on the whole domain for steady state and transient heat generation problems was compared to finite difference methods. The comparison consisted of the maximum absolute error from the exact solution and computer time required for solution. One steady state and one transient heat generation problem were solved by collocation and Galerkin weighted residual methods and finite differences. The least squares weighted residual method was also used for the steady state problem. Both problems were one-dimensional and had Dirichlet boundary conditions. Integrals for weighted residual methods were evaluated analytically to produce recursion relations. The transient problem was solved by the reduction to ordinary differential equations method for weighted residuals. The Galerkin method was fastest to a given accuracy for both problems evaluated. The accuracy of Galerkin and other weighted residual methods was greater than finite differences after a point at low solution accuracy. This crossover point was typically two to three digits of accuracy. The polynomial trial functions used for weighted residual solutions exhibited a numerical instability for solutions of 10 terms and over increasing the maximum absolute error. Orthogonal collocation and weighted residuals on finite elements were recommended as alternate methods. (Auhtor).

An Analysis of Weighted Residual Methods for Two Dimensional Flows

An Analysis of Weighted Residual Methods for Two Dimensional Flows Book
Author : B. R. Olmstead
Publisher : Unknown
Release : 1973
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download An Analysis of Weighted Residual Methods for Two Dimensional Flows book written by B. R. Olmstead, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

The Finite Element Method in Engineering

The Finite Element Method in Engineering Book
Author : Singiresu S. Rao
Publisher : Elsevier
Release : 2011-03-15
ISBN : 0080470505
Language : En, Es, Fr & De

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Book Description :

The Finite Element Method in Engineering is the only book to provide a broad overview of the underlying principles of finite element analysis and where it fits into the larger context of other mathematically based engineering analytical tools. This is an updated and improved version of a finite element text long noted for its practical applications approach, its readability, and ease of use. Students will find in this textbook a thorough grounding of the mathematical principles underlying the popular, analytical methods for setting up a finite element solution based on mathematical equations. The book provides a host of real-world applications of finite element analysis, from structural design to problems in fluid mechanics and thermodynamics. It has added new sections on the assemblage of element equations, as well as an important new comparison between finite element analysis and other analytical methods showing advantages and disadvantages of each. This book will appeal to students in mechanical, structural, electrical, environmental and biomedical engineering. The only book to provide a broadoverview of the underlying principles of finite element analysis and where it fits into the larger context of other mathematically based engineering analytical tools. New sections added on the assemblage of element equations, and an important new comparison between finite element analysis and other analytical methods, showing the advantages and disadvantages of each.

Weighted Residual Methods for Linear Fractional Differential Equations

Weighted Residual Methods for Linear Fractional Differential Equations Book
Author : Suha Najeeb Shihab,Ahmed Mohammed Shucker
Publisher : LAP Lambert Academic Publishing
Release : 2013
ISBN : 9783659463525
Language : En, Es, Fr & De

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Book Description :

In Chapter one, an introduction of the fractional calculus is presented. In Chapter two: gives the definition of expansion method and weighted residual methods. Also important theories and definitions concerning the converge and stability of methods for solving a system of equations are given in this chapter. In Chapter three Both fractional Fredholm integro-differential equations (FFIDE) and fractional Volterra integro-differential equations (FVIDE) will be solved using the weighted residual methods with the orthogonal functions as a basis functions to approximate the unknown function within the proposed methods. Several examples are included. In Chapter four Both FFIDE and FVIDE will be solved using the weighted residual methods with the spline functions as a basis functions to approximate the unknown function within the proposed methods. Several examples are included. Chapter five includes conclusions and recommendations for future work and comparisons with the methods are given in tables.

Finite Elements and Approximation

Finite Elements and Approximation Book
Author : O. C. Zienkiewicz,K. Morgan
Publisher : Courier Corporation
Release : 2013-04-22
ISBN : 048631801X
Language : En, Es, Fr & De

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Book Description :

A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises. Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher order finite element approximation, mapping and numerical integration, variational methods, and partial discretization and time-dependent problems. A survey of generalized finite elements and error estimates concludes the text.

Adaptive Finite Element Methods for Differential Equations

Adaptive Finite Element Methods for Differential Equations Book
Author : Wolfgang Bangerth,Rolf Rannacher
Publisher : Birkhäuser
Release : 2013-11-11
ISBN : 303487605X
Language : En, Es, Fr & De

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Book Description :

These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.

Comparisons of Piecewise Ritz and Weighted residual Methods

Comparisons of Piecewise Ritz and Weighted residual Methods Book
Author : Oscar E. Alvarez
Publisher : Unknown
Release : 1971
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Comparisons of Piecewise Ritz and Weighted residual Methods book written by Oscar E. Alvarez, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Introduction to Approximate Solution Techniques Numerical Modeling and Finite Element Methods

Introduction to Approximate Solution Techniques  Numerical Modeling  and Finite Element Methods Book
Author : Victor N. Kaliakin
Publisher : CRC Press
Release : 2018-04-19
ISBN : 135199090X
Language : En, Es, Fr & De

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Book Description :

Functions as a self-study guide for engineers and as a textbook for nonengineering students and engineering students, emphasizing generic forms of differential equations, applying approximate solution techniques to examples, and progressing to specific physical problems in modular, self-contained chapters that integrate into the text or can stand alone! This reference/text focuses on classical approximate solution techniques such as the finite difference method, the method of weighted residuals, and variation methods, culminating in an introduction to the finite element method (FEM). Discusses the general notion of approximate solutions and associated errors! With 1500 equations and more than 750 references, drawings, and tables, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods: Describes the approximate solution of ordinary and partial differential equations using the finite difference method Covers the method of weighted residuals, including specific weighting and trial functions Considers variational methods Highlights all aspects associated with the formulation of finite element equations Outlines meshing of the solution domain, nodal specifications, solution of global equations, solution refinement, and assessment of results Containing appendices that present concise overviews of topics and serve as rudimentary tutorials for professionals and students without a background in computational mechanics, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods is a blue-chip reference for civil, mechanical, structural, aerospace, and industrial engineers, and a practical text for upper-level undergraduate and graduate students studying approximate solution techniques and the FEM.

Application of Weighted Residual Methods to Metal Deformation Processing

Application of Weighted Residual Methods to Metal Deformation Processing Book
Author : Jaw-shyong Lan
Publisher : Unknown
Release : 1974
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Application of Weighted Residual Methods to Metal Deformation Processing book written by Jaw-shyong Lan, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Numerical Methods for Engineers and Scientists Second Edition

Numerical Methods for Engineers and Scientists  Second Edition  Book
Author : Joe D. Hoffman,Steven Frankel
Publisher : CRC Press
Release : 2001-05-31
ISBN : 9780824704438
Language : En, Es, Fr & De

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Book Description :

Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."

Application of Weighted Residual Methods to Dynamic Economic Models

Application of Weighted Residual Methods to Dynamic Economic Models Book
Author : Ellen R. McGrattan
Publisher : Unknown
Release : 1997
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Application of Weighted Residual Methods to Dynamic Economic Models book written by Ellen R. McGrattan, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

The Time and Parameter generalized Weighted Residual Method

The Time  and Parameter generalized Weighted Residual Method Book
Author : Jan Scheffel,Kungliga tekniska högskolan. Skolan för elektro- och systemteknik
Publisher : Unknown
Release : 2008
ISBN : 9789171788764
Language : En, Es, Fr & De

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Book Description :

Download The Time and Parameter generalized Weighted Residual Method book written by Jan Scheffel,Kungliga tekniska högskolan. Skolan för elektro- och systemteknik, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Minimum Weighted Residual Methods in Endogenous Growth Models

Minimum Weighted Residual Methods in Endogenous Growth Models Book
Author : Michael Kejak
Publisher : Unknown
Release : 2000
ISBN : 9788086288291
Language : En, Es, Fr & De

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Book Description :

Download Minimum Weighted Residual Methods in Endogenous Growth Models book written by Michael Kejak, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Comparative Study of Weighted Residual Methods Applied to a 2D Field Problem

Comparative Study of Weighted Residual Methods Applied to a 2D Field Problem Book
Author : Michael S. Lasky
Publisher : Unknown
Release : 1988
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Comparative Study of Weighted Residual Methods Applied to a 2D Field Problem book written by Michael S. Lasky, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

On the Properties of the Zienkiewicz Weighted Residual Methods

On the Properties of the Zienkiewicz Weighted Residual Methods Book
Author : R. Thomas,I. Gladwell,University of Manchester. Department of Mathematics
Publisher : Unknown
Release : 1992
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download On the Properties of the Zienkiewicz Weighted Residual Methods book written by R. Thomas,I. Gladwell,University of Manchester. Department of Mathematics, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

The Finite Element Method Using MATLAB

The Finite Element Method Using MATLAB Book
Author : Young W. Kwon,Hyochoong Bang
Publisher : CRC Press
Release : 2018-10-03
ISBN : 9781420041880
Language : En, Es, Fr & De

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Book Description :

Expanded to include a broader range of problems than the bestselling first edition, Finite Element Method Using MATLAB: Second Edition presents finite element approximation concepts, formulation, and programming in a format that effectively streamlines the learning process. It is written from a general engineering and mathematical perspective rather than that of a solid/structural mechanics basis. What's new in the Second Edition? Each chapter in the Second Edition now includes an overview that outlines the contents and purpose of each chapter. The authors have also added a new chapter of special topics in applications, including cracks, semi-infinite and infinite domains, buckling, and thermal stress. They discuss three different linearization techniques to solve nonlinear differential equations. Also included are new sections on shell formulations and MATLAB programs. These enhancements increase the book's already significant value both as a self-study text and a reference for practicing engineers and scientists.

Approximate Solutions of Clamped clamped Plates by the Weighted Residual Methods

Approximate Solutions of Clamped clamped Plates by the Weighted Residual Methods Book
Author : Asghar Nosier
Publisher : Unknown
Release : 1985
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Approximate Solutions of Clamped clamped Plates by the Weighted Residual Methods book written by Asghar Nosier, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

The Method of Weighted Residuals and Variational Principles

The Method of Weighted Residuals and Variational Principles Book
Author : Bruce A. Finlayson
Publisher : SIAM
Release : 2013-12-30
ISBN : 1611973244
Language : En, Es, Fr & De

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Book Description :

This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element method for more complex problems, and provides detailed information on error bounds. Problem sets make this book ideal for self-study or as a course text.