Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations PDF full book. Access full book title Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations by Sujaul Chowdhury. Download full books in PDF and EPUB format.
Author: Sujaul Chowdhury Publisher: CRC Press ISBN: 1000486117 Category : Mathematics Languages : en Pages : 112
Book Description
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.
Author: Sujaul Chowdhury Publisher: CRC Press ISBN: 1000486117 Category : Mathematics Languages : en Pages : 112
Book Description
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.
Author: Milan Kubicek Publisher: Courier Corporation ISBN: 0486463001 Category : Mathematics Languages : en Pages : 338
Book Description
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.
Author: Uri M. Ascher Publisher: SIAM ISBN: 9781611971231 Category : Mathematics Languages : en Pages : 620
Book Description
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.
Author: Sujaul Chowdhury Publisher: Chapman & Hall/CRC ISBN: 9781003204916 Category : Mathematics Languages : en Pages : 102
Book Description
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.
Author: A.K. Aziz Publisher: Academic Press ISBN: 1483267997 Category : Mathematics Languages : en Pages : 380
Book Description
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.
Author: Paul W. Eloe Publisher: World Scientific ISBN: 9814733482 Category : Mathematics Languages : en Pages : 249
Book Description
"This book is devoted to the study of solutions of nonlinear ODE boundary value problems as nonlinear interpolation problems. In 1967, Lasota and Opial showed that, under suitable hypotheses, if solutions of a second-order nonlinear differential equation passing through two distinct points are unique, when they exist, then, in fact, a solution passing through two distinct points does exist. That result, coupled with the pioneering work of Philip Hartman on what was then called unrestricted n-parameter families has stimulated 50 years of rapid development in the study of solutions of boundary value problems as nonlinear interpolation problems. The purpose of this book is two-fold. First, the results that have been generated in the past 50 years are collected for the first time to produce a comprehensive and coherent treatment of what is now a well-defined area of study in the qualitative theory of ordinary differential equations. Second, methods and technical tools are sufficiently exposed so that the interested reader can contribute to the study of nonlinear interpolation"--
Author: Herbert B. Keller Publisher: Courier Dover Publications ISBN: 0486835626 Category : Mathematics Languages : en Pages : 416
Book Description
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.
Author: Sujaul Chowdhury
Author: Sujaul Chowdhury
Author: Milan Kubicek
Author: Uri M. Ascher
Author: Sujaul Chowdhury
Author: A.K. Aziz
Author: Donald Greenspan
Author: Paul W. Eloe
Author: Leslie Fox
Author: Herbert B. Keller
Author: Václav Majer