Numerical Solutions Of Boundary Value Problems For Ordinary Differential Equations
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Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations
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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 1994-12-01
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 1994-12-01 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.
Numerical Solutions Of Boundary Value Problems For Ordinary Differential Equations
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Author : A.K. Aziz
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Numerical Solutions Of Boundary Value Problems For Ordinary Differential Equations written by A.K. Aziz and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.
Numerical Solutions Of Boundary Value Problems For Ordinary Differential Equations
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Author : National Science Foundation (United States)
language : en
Publisher:
Release Date : 1975
Numerical Solutions Of Boundary Value Problems For Ordinary Differential Equations written by National Science Foundation (United States) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
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 Solutions Of Boundary Value Problems Of Non Linear Differential Equations
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Author : Sujaul Chowdhury
language : en
Publisher: CRC Press
Release Date : 2021-10-25
Numerical Solutions Of Boundary Value Problems Of Non Linear Differential Equations written by Sujaul Chowdhury and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-25 with Mathematics categories.
The book presents in comprehensive detail numerical solutions to boundary value problems of a number of non-linear differential equations. Replacing derivatives by finite difference approximations in these differential equations leads to a system of non-linear algebraic equations which we have solved using Newton’s iterative method. In each case, we have also obtained Euler solutions and ascertained that the iterations converge to Euler solutions. We find that, except for the boundary values, initial values of the 1st iteration need not be anything close to the final convergent values of the numerical solution. Programs in Mathematica 6.0 were written to obtain the numerical solutions.
Numerical Methods For Two Point Boundary Value Problems
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Author : Herbert B. Keller
language : en
Publisher: Courier Dover Publications
Release Date : 2018-11-14
Numerical Methods For Two Point Boundary Value Problems written by Herbert B. Keller and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-14 with Mathematics categories.
Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition.
The Numerical Solution Of Two Point Boundary Problems In Ordinary Differential Equations
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Author : Leslie Fox
language : en
Publisher:
Release Date : 1957
The Numerical Solution Of Two Point Boundary Problems In Ordinary Differential Equations written by Leslie Fox and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Boundary value problems categories.
Numerical Solution Of Two Point Boundary Value Problems
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Author : Herbert B. Keller
language : en
Publisher: SIAM
Release Date : 1976-01-01
Numerical Solution Of Two Point Boundary Value Problems written by Herbert B. Keller and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-01-01 with Mathematics categories.
Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.
Numerical Solution Of Ordinary Differential Equations
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Author : Kendall Atkinson
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-24
Numerical Solution Of Ordinary Differential Equations written by Kendall Atkinson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-24 with Mathematics categories.
A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.
Differential Algebraic Equations
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Author : Peter Kunkel
language : en
Publisher: European Mathematical Society
Release Date : 2006
Differential Algebraic Equations written by Peter Kunkel and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Boundary value problems categories.
Differential-algebraic equations are a widely accepted tool for the modeling and simulation of constrained dynamical systems in numerous applications, such as mechanical multibody systems, electrical circuit simulation, chemical engineering, control theory, fluid dynamics and many others. This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differential-algebraic operators, generalized solutions, and differential equations on manifolds complement the theoretical treatment of initial value problems. Two major classes of numerical methods for differential-algebraic equations (Runge-Kutta and BDF methods) are discussed and analyzed with respect to convergence and order. A chapter is devoted to index reduction methods that allow the numerical treatment of general differential-algebraic equations. The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods. A survey of current software packages for differential-algebraic equations completes the text. The book is addressed to graduate students and researchers in mathematics, engineering and sciences, as well as practitioners in industry. A prerequisite is a standard course on the numerical solution of ordinary differential equations. Numerous examples and exercises make the book suitable as a course textbook or for self-study.