Numerical Boundary Value ODEs

1. Front Matter

   Pages i-xii

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2. Conditioning, dichotomy and related numerical considerations

   1. A Unified View of Some Recent Developments in the Numerical Solution of Bvodes

      • Robert D. Russell

      Pages 1-20

   2. The Role of Conditioning in Shooting Techniques

      • Frank de Hoog, Robert Mattheij

      Pages 21-54

   3. On Non-Invertible Boundary Value Problems

      • R. M. M. Mattheij, F. R. de Hoog

      Pages 55-75

   4. Riccati Transformations: When and How to Use?

      • Paul van Loon

      Pages 77-89

   5. Discretizations with Dichotomic Stability for Two-Point Boundary Value Problems

      • Roland England, Robert M. M. Mattheij

      Pages 91-106

3. Implementation aspects of various methods

   1. Improving the Performance of Numerical Methods for Two Point Boundary Value Problems

      • W. H. Enright

      Pages 107-119

   2. Reducing the Number of Variational Equations in the Implementation of Multiple Shooting

      • Fred T. Krogh, J. P. Keener, Wayne H. Enright

      Pages 121-135

   3. The Spline-Collocation and the Spline-Galerkin Methods for Orr-Sommerfeld Problem

      • A. G. Sleptsov

      Pages 137-147

4. Singular perturbation (‘stiff’) problems

   1. On the Simultaneous Use of Asymptotic and Numerical Methods to Solve Nonlinear Two Point Problems with Boundary and Interior Layers

      • Robert E. O’Malley Jr.

      Pages 149-172

   2. Two Families of Symmetric Difference Schemes for Singular Perturbation Problems

      • Uri Ascher

      Pages 173-191

   3. A Numerical Method for Singular Perturbation Problems with Turning Points

      • David L. Brown

      Pages 193-205

   4. Numerical solution of singular perturbed boundary value problems using a collocation method with tension splines

      • Maximilian R. Maier

      Pages 207-225

5. Bifurcation problems and delay differential equations

   1. Solving Boundary Value Problems for Functional Differential Equations by Collation

      • G. Bader

      Pages 227-243

   2. The Approximation of Simple Singularities

      • A. Griewank, G. W. Reddien

      Pages 245-259

   3. Calculating the Loss of Stability by Transient Methods, with Application to Parabolic Partial Differential Equations

      • R. Seydel

      Pages 261-270

   4. A Runge-Kutta-Nystrom Method for Delay Differential Equations

      • A. Bellen

      Pages 271-283

6. Special applications

   1. A Finite Difference Method for the Basic Stationary Semiconductor Device Equations

      • Peter A. Markowich

      Pages 285-301

   2. Solution of Premixed and Counterflow Diffusion Flame Problems by Adaptive Boundary Value Methods

      • Mitchell D. Smooke, James A. Miller, Robert J. Kee

      Pages 303-317

7. Back Matter

   Pages 318-318

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In the past few years, knowledge about methods for the numerical solution of two-point boundary value problems has increased significantly. Important theoretical and practical advances have been made in a number or fronts, although they are not adequately described in any tt'xt currently available. With this in mind, we organized an international workshop, devoted solely to this topic. Tht' workshop took place in Vancouver, B.C., Canada, in July 1()"13, 1984. This volume contains the refereed proceedings of the workshop. Contributions to the workshop were in two formats. There were a small number of invited talks (ten of which are presented in this proceedings); the other contributions were in the rorm or poster sessions, for which there was no parallel activity in the workshop. We had attemptt'd to cover a number of topics and objectives in the talks. As a result, the general review papt'rs of O'Malley and Russell are intended to take a broader perspective, while the other papers aremore specific. The contributions in this volume are divided (somewhat arbitrarily) into five groups. The first group concerns fundamental issues like conditioning and decoupling, which have only rect'ntly gained a proper appreciation of their centrality. Understanding of certain aspects or shooting methods ties in with these fundamental concepts. The papers of Russell, dt' Hoog and Mattheij all deal with these issues.

• Approximation
• Boundary value problem
• boundary element method
• differential equation
• partial differential equation
• ordinary differential equations

• The University of British Columbia, Vancouver, Canada

  Uri M. Ascher

• University of New Mexico, Albuquerque, USA

  Robert D. Russell

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