Numerical Methods for Two-Point Boundary-Value Problems by Keller, Herbert B. -- Read -- Imperial Library of Trantor

Index

Cover Title Page Dedication Copyright Page Preface to the Dover Edition Preface Contents Chapter 1 Introduction

1.1 Initial-Value Problems 1.2 Two-Point Boundary-Value Problems

1.2.1 Boundary-Value Problems for General Systems

1.3 Numerical Methods for Initial-Value Problems 1.4 Iterative Solution of Nonlinear Systems; Contracting Maps

Chapter 2 Initial-V Alue Methods (Shooting)

2.1 Linear Second-Order Equations and Systems 2.2 Nonlinear Second-Order Equations 2.3 Linear and Nonlinear Systems 2.4 Variants of Shooting; Parallel Shooting

2.4.1 Power Series

Chapter 3 Finite-Difference Methods

3.1 Linear Second-Order Equations

3.2 Nonlinear Second-Order Equations 3.3 Linear and Nonlinear Systems

Chapter 4 Integral-Equation Methods

Chapter 5 Eigenvalue Problems

5.1 Introduction; Sturm-Liouville Problems 5.2 Initial-Value Methods for Eigenvalue Problems 5.3 Finite-Difference Methods 5.4 Eigenvalue Problems for Integral Equations 5.5 Generalized Eigenvalue Problems

5.5.1 Poincaré Continuation, Continuity Methods

Chapter 6 Practical Examples and Computational Exercises

Introduction 6.1 Shooting; Lubrication Theory

6.1.1 Computing Exercise; Forced Flow

6.2 Finite Differences; Biophysics

6.2.1 h → 0 Extrapolation 6.2.2 Computing Exercise; Nonlinear Diffusivity

Appendix A Function Space Approximation Methods

A.1 Galerkin’s Method A.2 Collocation Methods A.3 Generalized Ritz Methods Bibliography Index

Appendix B Numerical Solution of Two-Point Boundary-Value Problems

B.1 Shooting Methods B.2 Finite Difference Methods B.3 Eigenvalue Problems B.4 Singular Problems

Appendix C Some Further Results