ENGLISH

Spectral Methods for Time-Dependent Problems: Analysis and Applications

By Jan S. Hesthaven , David Gottlieb , Professor Sigal Gottlieb

Book information

Publisher
Cambridge University Press
Year
2007
ISBN
0521792118, 9780521792110
Open Library ID
OL22743999M
Language
english
Format
PDF
Filesize
5 MB (5314960 bytes)
Series
Cambridge Monographs on Applied and Computational Mathematics
Pages
281\281
Time added
2011-01-06 10:13:16

Description

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 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.

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