Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners.
- Ideal for both graduate students and practitioners, including both basic theory and more rigorous developments
- Written from material which has been thoroughly and successfully class-tested by experienced authors
- No other text in print deals with this topic at a fundamental level and it includes material never before covered in book form
Read more
Reviews & endorsements
'The book is excellent and will be valuable for post-graduate students, researchers and scientists working in applied sciences and mainly in the numerical analysis of time-dependent problems. The thoroughness of the exposition, the clarity of the mathematical techniques and the variety of the problems and theoretical results that are presented and rigorously analyzed make this book a primary reference in the advanced numerical analysis of partial differential equations.' Mathematical Reviews

Customer reviews

Not yet reviewed
Be the first to review

Log in to review

Review was not posted due to profanity
×

, create a review

(If you're not , sign out)

Please enter the right captcha value

Please enter a star rating.

Your review must be a minimum of 12 words.

How do you rate this item?

Reviews must contain at least 12 words about the product.

×

Product details
- Date Published: January 2007
- format: Hardback
- isbn: 9780521792110
- length: 284 pages
- dimensions: 229 x 152 x 19 mm
- weight: 0.59kg
- contains: 50 b/w illus.
- availability: Available
Table of Contents
Introduction
1. From local to global approximation
2. Trigonometric polynomial approximation
3. Fourier spectral methods
4. Orthogonal polynomials
5. Polynomial expansions
6. Polynomial approximations theory for smooth functions
7. Polynomial spectral methods
8. Stability of polynomial spectral methods
9. Spectral methods for non-smooth problems
10. Discrete stability and time integration
11. Computational aspects
12. Spectral methods on general grids
Bibliography.
Look Inside

General Resources

Resources

Find resources associated with this title

Back to resources home

Type	Name	Unlocked *	Format	Size

Showing of

This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.

Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

If you are having problems accessing these resources please contact lecturers@cambridge.org.

Authors
Jan S. Hesthaven, Brown University, Rhode Island
Jan Hesthaven is a Professor of Applied Mathematics at Brown University.
Sigal Gottlieb, University of Massachusetts, Dartmouth
Sigal Gottlieb is an Associate Professor at the Department of Mathematics, University of Massachusetts, Dartmouth.
David Gottlieb, Brown University, Rhode Island
David Gottlieb is a Professor in the Division of Applied Mathematics, Brown University.