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 NUMERICAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS WITH DERIVATIVE BOUNDARY CONDITIONS written by SUJAUL CHOWDHURY and published by American Academic Press. This book was released on 2019-07-10 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for graduate students in Mathematics and Physics, this book contains an extensive illustration of the use of finite-difference method in numerically solving boundary value problems with derivative boundary conditions. A wide class of differential equations have been numerically solved in this book. We start with differential equations of elementary functions such as Hyperbolic, Cosine and Sine, and solve those of special functions like Hermite, Laguerre, Legendre and Bessel. Those of Airy functions AiryAi and AiryBi, of stationary localised wavepacket, of polar equation of motion under the gravitational interaction, of Quantum Mechanical problem of a particle in a 1D box have also been solved. Mathematica 6.0 has been used to solve system of linear equations that we encounter and to plot numerical data. The comparison with known analytic solutions shows nearly perfect agreement in almost every case. By reading this book, readers will become adept in using finite difference method in numerically solving boundary value problems with two known derivative boundary conditions.
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.
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 Bishop Keller and published by . This book was released on 1992 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brief, elementary yet rigorous account of practical numerical methods for solving very general two-point boundary-value problems. Advanced undergraduate level. Over 100 problems.
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 Spline Solutions of Higher Order Boundary Value Problems written by Parcha Kalyani and published by GRIN Verlag. This book was released on 2020-06-09 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doctoral Thesis / Dissertation from the year 2014 in the subject Mathematics - Applied Mathematics, , language: English, abstract: Some of the problems of real world phenomena can be described by differential equations involving the ordinary or partial derivatives with some initial or boundary conditions. To interpret the physical behavior of the problem it is necessary to know the solution of the differential equation. Unfortunately, it is not possible to solve some of the differential equations whether they are ordinary or partial with initial or boundary conditions through the analytical methods. When, we fail to find the solution of ordinary differential equation or partial differential equation with initial or boundary conditions through the analytical methods, one can obtain the numerical solution of such problems through the numerical methods up to the desired degree of accuracy. Of course, these numerical methods can also be applied to find the numerical solution of a differential equation which can be solved analytically. Several problems in natural sciences, social sciences, medicine, business management, engineering, particle dynamics, fluid mechanics, elasticity, heat transfer, chemistry, economics, anthropology and finance can be transformed into boundary value problems using mathematical modeling. A few problems in various fields of science and engineering yield linear and nonlinear boundary value problems of second order such as heat equation in thermal studies, wave equation in communication etc. Fifth-order boundary value problems generally arise in mathematical modeling of viscoelastic flows. The dynamo action in some stars may be modeled by sixth-order boundary-value problems. The narrow convecting layers bounded by stable layers which are believed to surround A-type stars may be modeled by sixth-order boundary value problems which arise in astrophysics. The seventh order boundary value problems generally arise in modeling induction motors with two rotor circuits. Various phenomena such as convection, flow in wind tunnels, lee waves, eddies, etc. can also be modeled by higher order boundary value problems.
Download or read book Numerical Solution of Nonlinear Boundary Value Problems with Applications written by Milan Kubíček and published by Prentice Hall. This book was released on 1983 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Value Problems written by David L. Powers and published by . This book was released on 1999 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary Value Problems, Fourth Edition, continues to be the leading text on boundary value problems and Fourier series. The author, David Powers, has written a thorough, theoretical overview of solving partial differential equations by the methods of separation of variables. The text is comprised of five comprehensive parts which include: a prerequisite summary of ordinary differential equations, Fourier series, and solving linear partial differential equations by separation of variable methods, by Laplace transform methods, and by numerical methods. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering problems.
Download or read book A Unified Approach to Boundary Value Problems written by Athanassios S. Fokas and published by SIAM. This book was released on 2008-11-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel approach to analysing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, based on ideas of the inverse scattering transform that the author introduced in 1997. This method is unique in also yielding novel integral representations for linear PDEs. Several new developments are addressed in the book, including a new transform method for linear evolution equations on the half-line and on the finite interval; analytical inversion of certain integrals such as the attenuated Radon transform and the Dirichlet-to-Neumann map for a moving boundary; integral representations for linear boundary value problems; analytical and numerical methods for elliptic PDEs in a convex polygon; and integrable nonlinear PDEs. An epilogue provides a list of problems on which the author's new approach has been used, offers open problems, and gives a glimpse into how the method might be applied to problems in three dimensions.
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 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:
Download or read book Numerical Methods for Problems in Infinite Domains written by D. Givoli and published by Elsevier. This book was released on 2013-10-22 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reviews and discusses the main numerical methods used today for solving problems in infinite domains. It also presents in detail one very effective method in this class, namely the Dirichlet-to-Neumann (DtN) finite element method. The book is intended to provide the researcher or engineer with the state-of-the-art in numerical solution methods for infinite domain problems, such as the problems encountered in acoustics and structural acoustics, fluid dynamics, meteorology, and many other fields of application. The emphasis is on the fundamentals of the various methods, and on reporting recent progress and forecasting future directions. An appendix at the end of the book provides an introduction to the essentials of the finite element method, and suggests a short list of texts on the subject which are categorized by their level of mathematics.
Download or read book The Fast Solution of Boundary Integral Equations written by Sergej Rjasanow and published by Springer Science & Business Media. This book was released on 2007-04-17 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.
Download or read book Boundary Value Problems Integral Equations And Related Problems Proceedings Of The International Conference written by Guo Chun Wen and published by World Scientific. This book was released on 2000-02-22 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this proceedings volume, the following topics are discussed: (1) various boundary value problems for partial differential equations and functional equations, including free and moving boundary problems; (2) the theory and methods of integral equations and integral operators, including singular integral equations; (3) applications of boundary value problems and integral equations to mechanics and physics; (4) numerical methods of integral equations and boundary value problems; and (5) some problems related with analysis and the foregoing subjects.
Download or read book Student Solutions Manual Boundary Value Problems written by David L. Powers and published by Academic Press. This book was released on 2009-07-13 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Student Solutions Manual, Boundary Value Problems
Download or read book Boundary Value Problems written by David L. Powers and published by Academic Press. This book was released on 2006 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface -- Chapter 0. Ordinary Differential Equations -- Chapter 1. Fourier Series and Integrals -- Chapter 2. The Heat Equation -- Chapter 3. The Wave Equation -- Chapter 4. The Potential Equation -- Chapter 5. Higher Dimensions & Other Coordinates.
