Author: Boško S. Jovanović
Publisher: Matematicki Institut
ISBN:
Category : Boundary value problems
Languages : en
Pages : 102
Book Description
The Finite Difference Method for Boundary-value Problems with Weak Solutions
Author: Boško S. Jovanović
Publisher: Matematicki Institut
ISBN:
Category : Boundary value problems
Languages : en
Pages : 102
Book Description
Publisher: Matematicki Institut
ISBN:
Category : Boundary value problems
Languages : en
Pages : 102
Book Description
The Finite Difference Method for Boundary-value Problems with Weak Solutions
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 91
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 91
Book Description
Finite Difference Methods for Ordinary and Partial Differential Equations
Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
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.
Publisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
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.
Numerical Solutions of Boundary Value Problems with Finite Difference Method
Author: Sujaul Chowdhury
Publisher: Morgan & Claypool
ISBN: 9781643272825
Category : Science
Languages : en
Pages : 88
Book Description
Containing an extensive illustration of the use of finite difference method in solving boundary value problem numerically, a wide class of differential equations have been numerically solved in this book.
Publisher: Morgan & Claypool
ISBN: 9781643272825
Category : Science
Languages : en
Pages : 88
Book Description
Containing an extensive illustration of the use of finite difference method in solving boundary value problem numerically, a wide class of differential equations have been numerically solved in this book.
Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations
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.
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.
Solving Ordinary and Partial Boundary Value Problems in Science and Engineering
Author: Karel Rektorys
Publisher: CRC Press
ISBN: 9780849325526
Category : Mathematics
Languages : en
Pages : 218
Book Description
This book provides an elementary, accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, acquainting readers with fundamental properties and with efficient methods of constructing solutions or satisfactory approximations. Discussions include: ordinary differential equations classical theory of partial differential equations Laplace and Poisson equations heat equation variational methods of solution of corresponding boundary value problems methods of solution for evolution partial differential equations The author presents special remarks for the mathematical reader, demonstrating the possibility of generalizations of obtained results and showing connections between them. For the non-mathematician, the author provides profound functional-analytical results without proofs and refers the reader to the literature when necessary. Solving Ordinary and Partial Boundary Value Problems in Science and Engineering contains essential functional analytical concepts, explaining its subject without excessive abstraction.
Publisher: CRC Press
ISBN: 9780849325526
Category : Mathematics
Languages : en
Pages : 218
Book Description
This book provides an elementary, accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, acquainting readers with fundamental properties and with efficient methods of constructing solutions or satisfactory approximations. Discussions include: ordinary differential equations classical theory of partial differential equations Laplace and Poisson equations heat equation variational methods of solution of corresponding boundary value problems methods of solution for evolution partial differential equations The author presents special remarks for the mathematical reader, demonstrating the possibility of generalizations of obtained results and showing connections between them. For the non-mathematician, the author provides profound functional-analytical results without proofs and refers the reader to the literature when necessary. Solving Ordinary and Partial Boundary Value Problems in Science and Engineering contains essential functional analytical concepts, explaining its subject without excessive abstraction.
Numerical Solution of Differential Equations
Author: Zhilin Li
Publisher: Cambridge University Press
ISBN: 1107163226
Category : Mathematics
Languages : en
Pages : 305
Book Description
A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
Publisher: Cambridge University Press
ISBN: 1107163226
Category : Mathematics
Languages : en
Pages : 305
Book Description
A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.
Numerical Solution of Two Point Boundary Value Problems
Author: Herbert B. Keller
Publisher: SIAM
ISBN: 0898710219
Category : Mathematics
Languages : en
Pages : 67
Book Description
Lectures on a unified theory of and practical procedures for the numerical solution of two point boundary-value problems.
Publisher: SIAM
ISBN: 0898710219
Category : Mathematics
Languages : en
Pages : 67
Book Description
Lectures on a unified theory of and practical procedures for the numerical solution of two point boundary-value problems.
Numerical Solution of Boundary Value Problems for Ordinary Differential Equations
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.
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.
Analysis of Finite Difference Schemes
Author: Boško S. Jovanović
Publisher: Springer Science & Business Media
ISBN: 1447154606
Category : Mathematics
Languages : en
Pages : 416
Book Description
This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.
Publisher: Springer Science & Business Media
ISBN: 1447154606
Category : Mathematics
Languages : en
Pages : 416
Book Description
This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.