Numerical Solution Of One Dimensional Heat Equation Using Finite Difference Method
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Numerical Solution Of One Dimensional Heat Equation Using Finite Difference Method
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Author : Nor Hazwani Mohammad
language : en
Publisher:
Release Date : 2012
Numerical Solution Of One Dimensional Heat Equation Using Finite Difference Method written by Nor Hazwani Mohammad and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Finite Difference Methods In Heat Transfer
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Author : M. Necati Özişik
language : en
Publisher: CRC Press
Release Date : 2017-07-12
Finite Difference Methods In Heat Transfer written by M. Necati Özişik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Science categories.
Finite Difference Methods in Heat Transfer presents a clear, step-by-step delineation of finite difference methods for solving engineering problems governed by ordinary and partial differential equations, with emphasis on heat transfer applications. The finite difference techniques presented apply to the numerical solution of problems governed by similar differential equations encountered in many other fields. Fundamental concepts are introduced in an easy-to-follow manner. Representative examples illustrate the application of a variety of powerful and widely used finite difference techniques. The physical situations considered include the steady state and transient heat conduction, phase-change involving melting and solidification, steady and transient forced convection inside ducts, free convection over a flat plate, hyperbolic heat conduction, nonlinear diffusion, numerical grid generation techniques, and hybrid numerical-analytic solutions.
Finite Difference Methods In Heat Transfer
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Author : M. Necati Özişik
language : en
Publisher: CRC Press
Release Date : 2017-07-20
Finite Difference Methods In Heat Transfer written by M. Necati Özişik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-20 with Science categories.
Finite Difference Methods in Heat Transfer, Second Edition focuses on finite difference methods and their application to the solution of heat transfer problems. Such methods are based on the discretization of governing equations, initial and boundary conditions, which then replace a continuous partial differential problem by a system of algebraic equations. Finite difference methods are a versatile tool for scientists and for engineers. This updated book serves university students taking graduate-level coursework in heat transfer, as well as being an important reference for researchers and engineering. Features Provides a self-contained approach in finite difference methods for students and professionals Covers the use of finite difference methods in convective, conductive, and radiative heat transfer Presents numerical solution techniques to elliptic, parabolic, and hyperbolic problems Includes hybrid analytical–numerical approaches
An Implicit Numerical Method For Solving The Two Dimensional Heat Equation
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Author : George A. Baker
language : en
Publisher:
Release Date : 1958
An Implicit Numerical Method For Solving The Two Dimensional Heat Equation written by George A. Baker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Heat equation categories.
Numerical Solution Of Differential Equations
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Author : Zhilin Li
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-30
Numerical Solution Of Differential Equations written by Zhilin Li and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-30 with Mathematics categories.
A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
Numerical Analysis Of Partial Differential Equations Using Maple And Matlab
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Author : Martin J. Gander
language : en
Publisher: SIAM
Release Date : 2018-08-06
Numerical Analysis Of Partial Differential Equations Using Maple And Matlab written by Martin J. Gander and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-06 with Science categories.
This book provides an elementary yet comprehensive introduction to the numerical solution of partial differential equations (PDEs). Used to model important phenomena, such as the heating of apartments and the behavior of electromagnetic waves, these equations have applications in engineering and the life sciences, and most can only be solved approximately using computers.? Numerical Analysis of Partial Differential Equations Using Maple and MATLAB provides detailed descriptions of the four major classes of discretization methods for PDEs (finite difference method, finite volume method, spectral method, and finite element method) and runnable MATLAB? code for each of the discretization methods and exercises. It also gives self-contained convergence proofs for each method using the tools and techniques required for the general convergence analysis but adapted to the simplest setting to keep the presentation clear and complete. This book is intended for advanced undergraduate and early graduate students in numerical analysis and scientific computing and researchers in related fields. It is appropriate for a course on numerical methods for partial differential equations.
The Finite Difference Method In Partial Differential Equations
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Author : A. R. Mitchell
language : en
Publisher:
Release Date : 1980-03-10
The Finite Difference Method In Partial Differential Equations written by A. R. Mitchell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-03-10 with Mathematics categories.
Extensively revised edition of Computational Methods in Partial Differential Equations. A more general approach has been adopted for the splitting of operators for parabolic and hyperbolic equations to include Richtmyer and Strang type splittings in addition to alternating direction implicit and locally one dimensional methods. A description of the now standard factorization and SOR/ADI iterative techniques for solving elliptic difference equations has been supplemented with an account or preconditioned conjugate gradient methods which are currently gaining in popularity. Prominence is also given to the Galerkin method using different test and trial functions as a means of constructing difference approximations to both elliptic and time dependent problems. The applications of finite difference methods have been revised and contain examples involving the treatment of singularities in elliptic equations, free and moving boundary problems, as well as modern developments in computational fluid dynamics. Emphasis throughout is on clear exposition of the construction and solution of difference equations. Material is reinforced with theoretical results when appropriate.
An Investigation Of The Method Of Finite Elements With Accuracy Comparisons To The Method Of Finite Differences For Solution Of The Transient Heat Conduction Equation Using Optimum Implicit Formulations
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Author : Joseph C. Geneczko
language : en
Publisher:
Release Date : 1978
An Investigation Of The Method Of Finite Elements With Accuracy Comparisons To The Method Of Finite Differences For Solution Of The Transient Heat Conduction Equation Using Optimum Implicit Formulations written by Joseph C. Geneczko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.
The one-dimensional transient heat conduction equation, with Dirichlet boundary conditions, is solved by the method of finite-elements, employing a quadratic interpolation function. The numerical solutions are investigated with respect to accuracy and stability, and compared to like results attained by the method of finite-differences, and the finite-element method with linear interpolation. The version of the finite-element method used was based on a variational principle which is stationary in time; the temporal behavior of the differential equation is treated with a finite-difference approximation. This method is equivalent to the method of Galerkin, called the Method of Weighted Residuals. The inherent discontinuity between the initial condition and boundary conditions was accounted for by substituting the exact analytical solution at the first time step and numerically computating from there. An equivalency relationship between the two finite-element methods is shown to exist. The finite-difference version of the Crank-Nicolson method is found to be more accurate than the finite-element version; for the fully implicit method, the opposite is found to be true. In the optimum implicit method, both finite-element solutions are shown equivalent to the finite-difference solution for a Fourier modulus of one. For other values of this parameter, the finite-element solution is more accurate. (Author).
Numerical Heat Transfer
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Author : Tien Mo Shih
language : en
Publisher: CRC Press
Release Date : 1984-06-01
Numerical Heat Transfer written by Tien Mo Shih and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-06-01 with Science categories.
Introduction To Approximate Solution Techniques Numerical Modeling And Finite Element Methods
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Author : Victor N. Kaliakin
language : en
Publisher: CRC Press
Release Date : 2001-09-25
Introduction To Approximate Solution Techniques Numerical Modeling And Finite Element Methods written by Victor N. Kaliakin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-25 with Technology & Engineering categories.
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.