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Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations
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Book Synopsis Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by : Uri M. Ascher
Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1994-12-01 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations by : A.K. Aziz
Download or read book Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations written by A.K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Solution of Nonlinear Boundary Value Problems with Applications by : Milan Kubicek
Download or read book Numerical Solution of Nonlinear Boundary Value Problems with Applications written by Milan Kubicek and published by Courier Corporation. This book was released on 2008-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Methods for Two-Point Boundary-Value Problems by : Herbert B. Keller
Download or read book Numerical Methods for Two-Point Boundary-Value Problems written by Herbert B. Keller and published by Courier Dover Publications. This book was released on 2018-11-14 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary yet rigorous, this concise treatment explores practical numerical methods for solving very general two-point boundary-value problems. The approach is directed toward students with a knowledge of advanced calculus and basic numerical analysis as well as some background in ordinary differential equations and linear algebra. After an introductory chapter that covers some of the basic prerequisites, the text studies three techniques in detail: initial value or "shooting" methods, finite difference methods, and integral equations methods. Sturm-Liouville eigenvalue problems are treated with all three techniques, and shooting is applied to generalized or nonlinear eigenvalue problems. Several other areas of numerical analysis are introduced throughout the study. The treatment concludes with more than 100 problems that augment and clarify the text, and several research papers appear in the Appendixes.
Book Synopsis Numerical Solution of Ordinary Differential Equations by : Kendall Atkinson
Download or read book Numerical Solution of Ordinary Differential Equations written by Kendall Atkinson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Numerical Solution of Two-point Boundary Problems in Ordinary Differential Equations by : Leslie Fox
Download or read book The Numerical Solution of Two-point Boundary Problems in Ordinary Differential Equations written by Leslie Fox and published by . This book was released on 1957 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of Two Point Boundary Value Problems by : Herbert B. Keller
Download or read book Numerical Solution of Two Point Boundary Value Problems written by Herbert B. Keller and published by SIAM. This book was released on 1976-01-01 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations by : National Science Foundation (United States)
Download or read book Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations written by National Science Foundation (United States) and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations by : Sujaul Chowdhury
Download or read book Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations written by Sujaul Chowdhury and published by CRC Press. This book was released on 2021-10-25 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Numerical Solution of Ordinary and Partial Differential Equations by : Granville Sewell
Download or read book The Numerical Solution of Ordinary and Partial Differential Equations written by Granville Sewell and published by World Scientific. This book was released on 2014-12-16 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A. The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions. Contents:Direct Solution of Linear SystemsInitial Value Ordinary Differential EquationsThe Initial Value Diffusion ProblemThe Initial Value Transport and Wave ProblemsBoundary Value ProblemsThe Finite Element MethodsAppendix A — Solving PDEs with PDE2DAppendix B — The Fourier Stability MethodAppendix C — MATLAB ProgramsAppendix D — Answers to Selected Exercises Readership: Undergraduate, graduate students and researchers. Key Features:The discussion of stability, absolute stability and stiffness in Chapter 1 is clearer than in other textsStudents will actually learn to write programs solving a range of simple PDEs using the finite element method in chapter 5In Appendix A, students will be able to solve quite difficult PDEs, using the author's software package, PDE2D. (a free version is available which solves small to moderate sized problems)Keywords:Differential Equations;Partial Differential Equations;Finite Element Method;Finite Difference Method;Computational Science;Numerical AnalysisReviews: "This book is very well written and it is relatively easy to read. The presentation is clear and straightforward but quite rigorous. This book is suitable for a course on the numerical solution of ODEs and PDEs problems, designed for senior level undergraduate or beginning level graduate students. The numerical techniques for solving problems presented in the book may also be useful for experienced researchers and practitioners both from universities or industry." Andrzej Icha Pomeranian Academy in Słupsk Poland
Book Synopsis The Numerical Solution of Ordinary and Partial Differential Equations by : Granville Sewell
Download or read book The Numerical Solution of Ordinary and Partial Differential Equations written by Granville Sewell and published by John Wiley & Sons. This book was released on 2005-07-25 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn to write programs to solve ordinary and partial differential equations The Second Edition of this popular text provides an insightful introduction to the use of finite difference and finite element methods for the computational solution of ordinary and partial differential equations. Readers gain a thorough understanding of the theory underlying themethods presented in the text. The author emphasizes the practical steps involved in implementing the methods, culminating in readers learning how to write programs using FORTRAN90 and MATLAB(r) to solve ordinary and partial differential equations. The book begins with a review of direct methods for the solution of linear systems, with an emphasis on the special features of the linear systems that arise when differential equations are solved. The following four chapters introduce and analyze the more commonly used finite difference methods for solving a variety of problems, including ordinary and partial differential equations and initial value and boundary value problems. The techniques presented in these chapters, with the aid of carefully developed exercises and numerical examples, can be easilymastered by readers. The final chapter of the text presents the basic theory underlying the finite element method. Following the guidance offered in this chapter, readers gain a solid understanding of the method and discover how to use it to solve many problems. A special feature of the Second Edition is Appendix A, which describes a finite element program, PDE2D, developed by the author. Readers discover how PDE2D can be used to solve difficult partial differential equation problems, including nonlinear time-dependent and steady-state systems, and linear eigenvalue systems in 1D intervals, general 2D regions, and a wide range of simple 3D regions. The software itself is available to instructors who adopt the text to share with their students.
Book Synopsis Numerical Solution of Boundary Value Problems in Ordinary Differential Equations [microform] by : Riaz Ahmad Usmani
Download or read book Numerical Solution of Boundary Value Problems in Ordinary Differential Equations [microform] written by Riaz Ahmad Usmani and published by National Library of Canada. This book was released on 1967 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Difference Methods for Ordinary and Partial Differential Equations by : Randall J. LeVeque
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Book Synopsis Codes for Boundary-Value Problems in Ordinary Differential Equations by : B. Childs
Download or read book Codes for Boundary-Value Problems in Ordinary Differential Equations written by B. Childs and published by Springer Science & Business Media. This book was released on 1979-10 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conceptually, a database consists of objects and relationships. Object Relationship Notation (ORN) is a simple notation that more precisely defines relationships by combining UML multiplicities with uniquely defined referential actions. Object Relationship Notation (ORN) for Database Applications: Enhancing the Modeling and Implementation of Associations shows how ORN can be used in UML class diagrams & database definition languages (DDLs) to better model & implement relationships & thus more productively develop database applications. For the database developer, it presents many examples of relationships modeled using ORN-extended class diagrams & shows how these relationships are easily mapped to an ORN-extended SQL or Object DDL. For the DBMS developer, it presents the specifications & algorithms needed to implement ORN in a relational and object DBMS. This book also describes tools that can be downloaded or accessed via the Web. These tools allow databases to be modeled using ORN and implemented using automatic code generation that adds ORN support to Microsoft SQL Server and Progress Object Store.
Book Synopsis Numerical Solution of Ordinary Differential Equations by : L.F. Shampine
Download or read book Numerical Solution of Ordinary Differential Equations written by L.F. Shampine and published by Routledge. This book was released on 2018-10-24 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods.
Book Synopsis Numerical Solution of Ordinary Differential Equations by : L. Fox
Download or read book Numerical Solution of Ordinary Differential Equations written by L. Fox and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numerical solution ofordinary differential equations, numerical solution of partial differential equations, and so on. These are needed because our numerical education and software have improved and because our relevant problems exhibit more variety and more difficulty. Ordinary differential equa tions are obvious candidates for such treatment, and the current book is written in this sense.
Book Synopsis Numerical Solution of Initial-value Problems in Differential-algebraic Equations by : K. E. Brenan
Download or read book Numerical Solution of Initial-value Problems in Differential-algebraic Equations written by K. E. Brenan and published by SIAM. This book was released on 1996-01-01 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. This classic edition, originally published in 1989, is the only general DAE book available. It not only develops guidelines for choosing different numerical methods, it is the first book to discuss DAE codes, including the popular DASSL code. An extensive discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAE's. New to this edition is a chapter that brings the discussion of DAE software up to date. The objective of this monograph is to advance and consolidate the existing research results for the numerical solution of DAE's. The authors present results on the analysis of numerical methods, and also show how these results are relevant for the solution of problems from applications. They develop guidelines for problem formulation and effective use of the available mathematical software and provide extensive references for further study.
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