June 17, 2021

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Weighted Residual Methods

Weighted Residual Methods
Author : Mohammad Hatami
Publisher : Academic Press
Release Date : 2017-11-07
Category : Technology & Engineering
Total pages :384
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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

The Method of Weighted Residuals and Variational Principles

The Method of Weighted Residuals and Variational Principles
Author : Bruce A. Finlayson
Publisher : SIAM
Release Date : 2013-12-30
Category : Mathematics
Total pages :412
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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.

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
Author : Robert Earl Naegeli,AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING.
Publisher : Unknown
Release Date : 1982
Category :
Total pages :99
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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
Author : B. R. Olmstead
Publisher : Unknown
Release Date : 1973
Category :
Total pages :175
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Minimum weighted residual methods in endogeneous growth models

Minimum weighted residual methods in endogeneous growth models
Author : Michal Kejak
Publisher : Unknown
Release Date : 2000
Category : Economic development
Total pages :10
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Finite Elements and Approximation

Finite Elements and Approximation
Author : O. C. Zienkiewicz,K. Morgan
Publisher : Courier Corporation
Release Date : 2013-04-22
Category : Technology & Engineering
Total pages :352
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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.

WEIGHTED-RESIDUAL METHODS IN SPACE-DEPENDENT REACTOR DYNAMICS.

WEIGHTED-RESIDUAL METHODS IN SPACE-DEPENDENT REACTOR DYNAMICS.
Author : Anonim
Publisher : Unknown
Release Date : 1969
Category :
Total pages :129
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Minimum Weighted Residual Methods in Endogenous Growth Models

Minimum Weighted Residual Methods in Endogenous Growth Models
Author : Michael Kejak
Publisher : Unknown
Release Date : 2000
Category : Economic development
Total pages :10
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Application of Weighted Residual Methods to Metal Deformation Processing

Application of Weighted Residual Methods to Metal Deformation Processing
Author : Jaw-shyong Lan
Publisher : Unknown
Release Date : 1974
Category : Deformations (Mechanics)
Total pages :250
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Approximate Solutions of Clamped-clamped Plates by the Weighted Residual Methods

Approximate Solutions of Clamped-clamped Plates by the Weighted Residual Methods
Author : Asghar Nosier
Publisher : Unknown
Release Date : 1985
Category :
Total pages :162
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Application of Weighted-residual Methods to Investigate the Nonlinear Dynamics of Boiling Water Reactors

Application of Weighted-residual Methods to Investigate the Nonlinear Dynamics of Boiling Water Reactors
Author : Brian Damiano
Publisher : Unknown
Release Date : 1992
Category : Boiling water reactors
Total pages :512
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Numerical Methods for Engineers and Scientists, Second Edition,

Numerical Methods for Engineers and Scientists, Second Edition,
Author : Joe D. Hoffman,Steven Frankel
Publisher : CRC Press
Release Date : 2001-05-31
Category : Mathematics
Total pages :840
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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."

On the Properties of the Zienkiewicz Weighted Residual Methods

On the Properties of the Zienkiewicz Weighted Residual Methods
Author : R. Thomas,I. Gladwell,University of Manchester. Department of Mathematics
Publisher : Unknown
Release Date : 1992
Category : Mathematics
Total pages :129
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Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods

Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods
Author : Victor N. Kaliakin
Publisher : CRC Press
Release Date : 2018-04-19
Category : Technology & Engineering
Total pages :664
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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.

Comparisons of Piecewise Ritz and Weighted-residual Methods

Comparisons of Piecewise Ritz and Weighted-residual Methods
Author : Oscar E. Alvarez
Publisher : Unknown
Release Date : 1971
Category :
Total pages :86
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