Computer Methods for Ordinary Differential Equations and Differential–Algebraic Equations

Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This is a practical and mathematically well informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included.

Preface; Part I. Introduction: 1. Ordinary differential equations; Part II. Initial Value Problems: 2. On problem stability; 3. Basic methods, basic concepts; 4. One-step methods; 5. Linear multistep methods; Part III. Boundary Value Problems: 6. More boundary value problem theory and applications; 7. Shooting; 8. Finite difference methods for boundary value problems; Part IV. Differential-Algebraic Equations: 9. More on differential-algebraic equations; 10. Numerical methods for differential-algebraic equations; Bibliography; Index.

Designed for anyone who wishes to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. A thorough understanding of the issues and methods for practical computation is provided, whilst avoiding an extensive theorem-proof exposition.