Finite Difference Methods for Ordinary and Partial Differential Equations
Finite Difference Methods for Ordinary and Partial Differential Equations
£57.99
GBPThis 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. Exercises and student projects are available on the book's webpage, along with Matlab mfiles for implementing methods. Readers will gain an understanding of the essential ideas that underlie the development, analysis, and practical use of finite difference methods as well as the key concepts of stability theory, their relation to one another, and their practical implications. The author provides a foundation from which students can approach more advanced topics.
- Addresses both steady-state boundary value problems and time-dependent problems
- Appendices provided covering concepts pertinent to Parts I and II
- Designed as an introductory graduate-level textbook on finite difference methods and their analysis; exercises projects and Matlab code available via web
Product details
September 2007Paperback
9780898716290
184 pages
254 × 178 × 18 mm
0.64kg
120 exercises
Available
Table of Contents
- Preface
- Part I. Boundary Value Problems and Iterative Methods:
- 1. Finite difference approximations
- 2. Steady states and boundary value problems
- 3. Elliptic equations
- 4. Iterative methods for sparse linear systems
- Part II. Initial Value Problems
- 5. The initial value problem for ordinary differential equations
- 6. Zero-stability and convergence for initial value problems
- 7. Absolute stability for ordinary differential equations
- 8. Stiff ordinary differential equations
- 9. Diffusion equations and parabolic problems
- 10. Advection equations and hyperbolic systems
- 11. Mixed equations
- A. Measuring errors
- B. Polynomial interpolation and orthogonal polynomials
- C. Eigenvalues and inner-product norms
- D. Matrix powers and exponentials
- E. Partial differential equations
- Bibliography
- Index.
