Numerical Solution Of Nonlinear Boundary Value Problems With Applications
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Numerical Solution Of Nonlinear Boundary Value Problems With Applications
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Author : Milan Kubicek
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
Numerical Solution Of Nonlinear Boundary Value Problems With Applications written by Milan Kubicek and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.
Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations
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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 1988-01-01
Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Unified Transform For Boundary Value Problems
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Author : Athanasios S. Fokas
language : en
Publisher: SIAM
Release Date : 2014-12-30
Unified Transform For Boundary Value Problems written by Athanasios S. Fokas and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-30 with Mathematics categories.
This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs.? The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Numerical Approximation Methods For Elliptic Boundary Value Problems
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Author : Olaf Steinbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-22
Numerical Approximation Methods For Elliptic Boundary Value Problems written by Olaf Steinbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-22 with Mathematics categories.
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.
Augmented Lagrangian Methods
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Author : M. Fortin
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Augmented Lagrangian Methods written by M. Fortin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.
The purpose of this volume is to present the principles of the Augmented Lagrangian Method, together with numerous applications of this method to the numerical solution of boundary-value problems for partial differential equations or inequalities arising in Mathematical Physics, in the Mechanics of Continuous Media and in the Engineering Sciences.
Numerical Solution Of Field Problems In Continuum Physics
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Author : Society for Industrial and Applied Mathematics
language : en
Publisher: American Mathematical Soc.
Release Date : 1970
Numerical Solution Of Field Problems In Continuum Physics written by Society for Industrial and Applied Mathematics and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
Numerical Solution Of Initial Value Problems In Differential Algebraic Equations
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Author : K. E. Brenan
language : en
Publisher: SIAM
Release Date : 1996-01-01
Numerical Solution Of Initial Value Problems In Differential Algebraic Equations written by K. E. Brenan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
This book describes some of the places where differential-algebraic equations (DAE's) occur.
Wavelet Numerical Method And Its Applications In Nonlinear Problems
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Author : You-He Zhou
language : en
Publisher: Springer Nature
Release Date : 2021-03-09
Wavelet Numerical Method And Its Applications In Nonlinear Problems written by You-He Zhou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-09 with Technology & Engineering categories.
This book summarizes the basic theory of wavelets and some related algorithms in an easy-to-understand language from the perspective of an engineer rather than a mathematician. In this book, the wavelet solution schemes are systematically established and introduced for solving general linear and nonlinear initial boundary value problems in engineering, including the technique of boundary extension in approximating interval-bounded functions, the calculation method for various connection coefficients, the single-point Gaussian integration method in calculating the coefficients of wavelet expansions and unique treatments on nonlinear terms in differential equations. At the same time, this book is supplemented by a large number of numerical examples to specifically explain procedures and characteristics of the method, as well as detailed treatments for specific problems. Different from most of the current monographs focusing on the basic theory of wavelets, it focuses on the use of wavelet-based numerical methods developed by the author over the years. Even for the necessary basic theory of wavelet in engineering applications, this book is based on the author’s own understanding in plain language, instead of a relatively difficult professional mathematical description. This book is very suitable for students, researchers and technical personnel who only want to need the minimal knowledge of wavelet method to solve specific problems in engineering.
The Optimal Homotopy Asymptotic Method
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Author : Vasile Marinca
language : en
Publisher: Springer
Release Date : 2015-04-02
The Optimal Homotopy Asymptotic Method written by Vasile Marinca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-02 with Technology & Engineering categories.
This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Two Point Boundary Value Problems
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Author : Colette De Coster
language : en
Publisher: Elsevier Science Limited
Release Date : 2006
Two Point Boundary Value Problems written by Colette De Coster and has been published by Elsevier Science Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction. Key features: - Presentation of the fundamental features of the method - Actual construction of lower and upper solutions in problems - Working applications - Illustrate theorems by examples - Description of the history of the method - Bibliographical notes Key features: - Presentation of the fundamental features of the method - Actual construction of lower and upper solutions in problems - Working applications - Illustrate theorems by examples - Description of the history of the method - Bibliographical notes