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.
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 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Discrete Numerical Methods in Physics and Engineering written by Greenspan and published by Academic Press. This book was released on 1974-05-31 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete Numerical Methods in Physics and Engineering
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.
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.
Download or read book Numerical Solution of Discrete Boundary Value Problems written by and published by . This book was released on 1995 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: This project concerned numerical methods for solving linear systems of equations of the type arising from discretization of boundary value problems of elliptic and mixed type. The problems considered were of fundamental use in mathematical models used in structural analysis and fluid dynamics. The emphasis was on preconditioning techniques in which properties of the problem are used to construct approximations that are easy to compute with and that lead to rapid convergence of iterative methods. The approach included both analytic studies producing bounds on convergence rates and computational experiments that confirm and supplement the analysis. (AN).
Download or read book Solving Differential Equations by Multistep Initial and Boundary Value Methods written by L Brugnano and published by CRC Press. This book was released on 1998-05-22 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical approximation of solutions of differential equations has been, and continues to be, one of the principal concerns of numerical analysis and is an active area of research. The new generation of parallel computers have provoked a reconsideration of numerical methods. This book aims to generalize classical multistep methods for both initial and boundary value problems; to present a self-contained theory which embraces and generalizes the classical Dahlquist theory; to treat nonclassical problems, such as Hamiltonian problems and the mesh selection; and to select appropriate methods for a general purpose software capable of solving a wide range of problems efficiently, even on parallel computers.
Download or read book Numerical Approximation Methods for Elliptic Boundary Value Problems written by Olaf Steinbach and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On the Numerical Solution of Two point Boundary Value Problems written by Yale University. Department of Computer Science and published by . This book was released on 1989 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "In this paper, we present a new numerical method for the solution of linear two-point boundary value problems of ordinary differential equations. After reducing the differential equation to a second kind integral equation, we discretize the latter via a high order Nyström scheme. A somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system using O(N [multiplied by] p[superscript 2]) operations, where N is the number of nodes on the interval and p is the desired order of convergence. Thus, the advantages of the integral equation formulation (small condition number, insensitivity to boundary layers, insensitivity to end-point singularities, etc.) are retained, while achieving a computational efficiency previously available only to finite difference or finite element methods."
Download or read book Numerical Methods in Fluid Dynamics written by Gary A. Sod and published by Cambridge University Press. This book was released on 1985-10-31 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous treatment of the techniques, beginning with the classical methods and leading to a discussion of modern developments. For easier reading and use, many of the purely technical results and theorems are given separately from the main body of the text. The presentation is intended for graduate students in applied mathematics, engineering and physical sciences who have a basic knowledge of partial differential equations.
Download or read book The Method of Summary Representation for Numerical Solution of Problems of Mathematical Physics written by G. N. Polozhii and published by Elsevier. This book was released on 2014-07-10 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pure and Applied Mathematics, Volume 79: The Method of Summary Representation for Numerical Solution of Problems of Mathematical Physics presents the numerical solution of two-dimensional and three-dimensional boundary-value problems of mathematical physics. This book focuses on the second-order and fourth-order linear differential equations. Organized into two chapters, this volume begins with an overview of ordinary finite-difference equations and the general solutions of certain specific finite-difference equations. This text then examines the various methods of successive approximation that are used exclusively for solving finite-difference equations. This book discusses as well the established formula of summary representation for certain finite-difference operators that are associated with partial differential equations of mathematical physics. The final chapter deals with the formula of summary representation to enable the researcher to write the solution of the corresponding systems of linear algebraic equations in a simple form. This book is a valuable resource for mathematicians and physicists.
Download or read book Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.
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 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Numerical analytic Methods In Theory Of Boundary Value Problems written by Miklos Ronto and published by World Scientific. This book was released on 2000-06-30 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory — namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs.The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with the classical Cesari, Cesari-Hale and Lyapunov-Schmidt methods.
Download or read book Approximation of Elliptic Boundary Value Problems written by Jean-Pierre Aubin and published by Courier Corporation. This book was released on 2007-01-01 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: A marriage of the finite-differences method with variational methods for solving boundary-value problems, the finite-element method is superior in many ways to finite-differences alone. This self-contained text for advanced undergraduates and graduate students is intended to imbed this combination of methods into the framework of functional analysis and to explain its applications to approximation of nonhomogeneous boundary-value problems for elliptic operators. The treatment begins with a summary of the main results established in the book. Chapter 1 introduces the variational method and the finite-difference method in the simple case of second-order differential equations. Chapters 2 and 3 concern abstract approximations of Hilbert spaces and linear operators, and Chapters 4 and 5 study finite-element approximations of Sobolev spaces. The remaining four chapters consider several methods for approximating nonhomogeneous boundary-value problems for elliptic operators.
