Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations - 1st Edition - ISBN: 9780120686605, 9781483267999

Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations

1st Edition

Editors: A.K. Aziz
eBook ISBN: 9781483267999
Imprint: Academic Press
Published Date: 28th January 1975
Page Count: 380
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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.

Table of Contents



Part I. Survey Lectures

Numerical Solutions of Initial Value Problems for Ordinary Differential Equations

Numerical Solution of Boundary Value Problems for Ordinary Differential Equations: Survey and Some Recent Results on Difference Methods

On the Conversion of Boundary-Value Problems into Stable Initial-Value Problems via Several Invariant Imbedding Algorithms

Part II. Invited Talks

The Connection between the Finite Difference Like Methods and the Methods Based on Initial Value Problems for ODE

A Smooth and Local Interpolant with “Small” K-th Derivative

Difference Approximations for Singular Perturbation Problems

The Occurrence and Solution of Boundary Value Reaction Systems

Invariant Imbedding for Fixed and Free Two Point Boundary Value Problems

A Posteriori Error Estimates

Boundary Problem Solvers for First Order Systems Based on Deferred Corrections

Numerical Solution of Boundary Value Problems by Stable Methods Based on the Transfer of Conditions

A Tale of Two Methods for Solving Two-Point Boundary Value Problems

Part III. Short Communications

Some Considerations in the Numerical Simulation of a Semiconductor Device

Comparison of Some Codes for the Initial Value Problem for Ordinary Differential Equations

A High-Order Finite-Difference Method for the Solution of Two-Point Boundary-Value Problems on a Uniform Mesh


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© Academic Press 1975
Academic Press
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About the Editor

A.K. Aziz

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