Boundary Value Problems for Second-Order Finite Difference Equations and Systems PDF Download
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Author: Johnny Henderson
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111040453
Category : Mathematics
Languages : en
Pages : 120
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Book Description
This is an indispensable reference for those mathematicians that conduct research activity in applications of fixed-point theory to boundary value problems for nonlinear difference equations. Coverage includes second-order finite difference equations and systems of second-order finite difference equations subject to diverse multi-point boundary conditions, and various methods to study the existence of positive solutions for these problems.
Author: Johnny Henderson
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111040453
Category : Mathematics
Languages : en
Pages : 120
Get Book
Book Description
This is an indispensable reference for those mathematicians that conduct research activity in applications of fixed-point theory to boundary value problems for nonlinear difference equations. Coverage includes second-order finite difference equations and systems of second-order finite difference equations subject to diverse multi-point boundary conditions, and various methods to study the existence of positive solutions for these problems.
Author: A.K. Aziz
Publisher: Academic Press
ISBN: 1483267997
Category : Mathematics
Languages : en
Pages : 380
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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: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
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Book Description
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.
Author: Johnny Henderson
Publisher: Academic Press
ISBN: 0128036796
Category : Mathematics
Languages : en
Pages : 322
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Book Description
Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditions Discusses second order difference equations with multi-point boundary conditions Introduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions
Author: Richard B. Philips
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 56
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Book Description
"This paper discusses a class of compact second order accurate finite difference equations for mixed initial-boundary value problems for hyperbolic and convective-diffusion equations. Convergence is proved by means of an energy argument and both types of equations are solved by similar algorithms. For hyperbolic equations an extension of the Lax-Wendroff method is described which incorporates dissipative boundary conditions. Upwind-downwind differencing techniques arise as the formal hyperbolic limit of the convective-diffusion equation. Finally, a finite difference 'chain-rule' transforms the schemes from rectangular to quadrilateral subdomains" -- abstract.
Author: Johnny Henderson
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111040372
Category : Mathematics
Languages : en
Pages : 168
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Book Description
This is an indispensable reference for those mathematicians that conduct research activity in applications of fixed-point theory to boundary value problems for nonlinear functional equations. Coverage includes second-order finite difference equations and systems of difference equations subject to multi-point boundary conditions, various methods to study the existence of positive solutions for difference equations, and Green functions.
Author: Uri M. Ascher
Publisher: SIAM
ISBN: 9781611971231
Category : Mathematics
Languages : en
Pages : 620
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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: J.W. Thomas
Publisher: Springer Science & Business Media
ISBN: 0387979999
Category : Mathematics
Languages : en
Pages : 460
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Book Description
What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.
Author: John C. Strikwerda
Publisher: Springer
ISBN:
Category : Juvenile Nonfiction
Languages : en
Pages : 410
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Book Description
Author: Granville Sewell
Publisher: Academic Press
ISBN: 1483259145
Category : Mathematics
Languages : en
Pages : 284
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Book Description
The Numerical Solution of Ordinary and Partial Differential Equations is an introduction to the numerical solution of ordinary and partial differential equations. Finite difference methods for solving partial differential equations are mostly classical low order formulas, easy to program but not ideal for problems with poorly behaved solutions or (especially) for problems in irregular multidimensional regions. FORTRAN77 programs are used to implement many of the methods studied. Comprised of six chapters, this book begins with a review of direct methods for the solution of linear systems, with emphasis on the special features of the linear systems that arise when differential equations are solved. The next four chapters deal with the more commonly used finite difference methods for solving a variety of problems, including both ordinary differential equations and partial differential equations, and both initial value and boundary value problems. The final chapter is an overview of the basic ideas behind the finite element method and covers the Galerkin method for boundary value problems. Examples using piecewise linear trial functions, cubic hermite trial functions, and triangular elements are presented. This monograph is appropriate for senior-level undergraduate or first-year graduate students of mathematics.
