Numerical Boundary Value Odes
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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 Boundary Value Odes
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Author : Ascher
language : en
Publisher: Birkhäuser
Release Date : 2011-10-01
Numerical Boundary Value Odes written by Ascher and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-01 with Mathematics categories.
In the past few years, knowledge about methods for the numerical solution of two-point boundary value problems has increased significantly. Important theoretical and practical advances have been made in a number or fronts, although they are not adequately described in any tt'xt currently available. With this in mind, we organized an international workshop, devoted solely to this topic. Tht' workshop took place in Vancouver, B.C., Canada, in July 1()"13, 1984. This volume contains the refereed proceedings of the workshop. Contributions to the workshop were in two formats. There were a small number of invited talks (ten of which are presented in this proceedings); the other contributions were in the rorm or poster sessions, for which there was no parallel activity in the workshop. We had attemptt'd to cover a number of topics and objectives in the talks. As a result, the general review papt'rs of O'Malley and Russell are intended to take a broader perspective, while the other papers are more specific. The contributions in this volume are divided (somewhat arbitrarily) into five groups. The first group concerns fundamental issues like conditioning and decoupling, which have only rect'ntly gained a proper appreciation of their centrality. Understanding of certain aspects or shooting methods ties in with these fundamental concepts. The papers of Russell, dt' Hoog and Mattheij all deal with these issues.
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 Boundary Value Odes
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Author : Ascher
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Boundary Value Odes written by Ascher 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 2012-12-06 with Mathematics categories.
In the past few years, knowledge about methods for the numerical solution of two-point boundary value problems has increased significantly. Important theoretical and practical advances have been made in a number or fronts, although they are not adequately described in any tt'xt currently available. With this in mind, we organized an international workshop, devoted solely to this topic. Tht' workshop took place in Vancouver, B.C., Canada, in July 1()"13, 1984. This volume contains the refereed proceedings of the workshop. Contributions to the workshop were in two formats. There were a small number of invited talks (ten of which are presented in this proceedings); the other contributions were in the rorm or poster sessions, for which there was no parallel activity in the workshop. We had attemptt'd to cover a number of topics and objectives in the talks. As a result, the general review papt'rs of O'Malley and Russell are intended to take a broader perspective, while the other papers are more specific. The contributions in this volume are divided (somewhat arbitrarily) into five groups. The first group concerns fundamental issues like conditioning and decoupling, which have only rect'ntly gained a proper appreciation of their centrality. Understanding of certain aspects or shooting methods ties in with these fundamental concepts. The papers of Russell, dt' Hoog and Mattheij all deal with these issues.
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.
Exact Finite Difference Schemes
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Author : Sergey Lemeshevsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-09-26
Exact Finite Difference Schemes written by Sergey Lemeshevsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-26 with Mathematics categories.
Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography
Codes For Boundary Value Problems In Ordinary Differential Equations
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Author : B. Childs
language : en
Publisher: Springer Science & Business Media
Release Date : 1979-10
Codes For Boundary Value Problems In Ordinary Differential Equations written by B. Childs 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 1979-10 with Computers categories.
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.
Applied Differential Equations With Boundary Value Problems
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Author : Vladimir Dobrushkin
language : en
Publisher: CRC Press
Release Date : 2017-10-19
Applied Differential Equations With Boundary Value Problems written by Vladimir Dobrushkin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.
Applied Differential Equations with Boundary Value Problems presents a contemporary treatment of ordinary differential equations (ODEs) and an introduction to partial differential equations (PDEs), including their applications in engineering and the sciences. This new edition of the author’s popular textbook adds coverage of boundary value problems. The text covers traditional material, along with novel approaches to mathematical modeling that harness the capabilities of numerical algorithms and popular computer software packages. It contains practical techniques for solving the equations as well as corresponding codes for numerical solvers. Many examples and exercises help students master effective solution techniques, including reliable numerical approximations. This book describes differential equations in the context of applications and presents the main techniques needed for modeling and systems analysis. It teaches students how to formulate a mathematical model, solve differential equations analytically and numerically, analyze them qualitatively, and interpret the results.
Finite Difference Methods For Ordinary And Partial Differential Equations
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Author : Randall J. LeVeque
language : en
Publisher: SIAM
Release Date : 2007-01-01
Finite Difference Methods For Ordinary And Partial Differential Equations written by Randall J. LeVeque and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
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.
The Numerical Solution Of Boundary Value Problems On Long Intervals
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Author : Peter A. Markowich
language : en
Publisher:
Release Date : 1981
The Numerical Solution Of Boundary Value Problems On Long Intervals written by Peter A. Markowich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
This paper deals with the numerical solution of boundary value problems of ordinary differential equations posed on infinite intervals. The solution of these problems proceeds in two steps. The first is to cut the infinite interval at a finite, large enough point and to insert additional, so called asymptotic boundary conditions at the far (right) end; the second is to solve the resulting two point boundary value problem by a numerical method, for example a difference scheme. In this paper the Box-scheme is investigated. Numerical problems arise, because standard algorithms use too many grid points as the length of the interval increases. An 'asymptotic' a priori mesh size sequence which increases exponentially, and which therefore only employs a reasonable number of meshpoints, is developed. Through investigating the conditioning of the (linearized) Box-scheme, we find that the solutions can be obtained safely by the Newton procedure when partial pivoting is employed.