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Spectral Methods for Time-Dependent Problems Jan S. Hesthaven (Brown University, Rhode Island)

Spectral Methods for Time-Dependent Problems By Jan S. Hesthaven (Brown University, Rhode Island)

Spectral Methods for Time-Dependent Problems by Jan S. Hesthaven (Brown University, Rhode Island)


Summary

Spectral methods are useful techniques for solving integral and partial differential equations, many of which appear in fluid mechanics and engineering problems. Based on a graduate course, this 2007 book presents these popular and efficient techniques with both rigorous analysis and extensive coverage of their wide range of applications.

Spectral Methods for Time-Dependent Problems Summary

Spectral Methods for Time-Dependent Problems by Jan S. Hesthaven (Brown University, Rhode Island)

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.

Spectral Methods for Time-Dependent Problems Reviews

'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

About Jan S. Hesthaven (Brown University, Rhode Island)

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

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.

Additional information

NPB9780521792110
9780521792110
0521792118
Spectral Methods for Time-Dependent Problems by Jan S. Hesthaven (Brown University, Rhode Island)
New
Hardback
Cambridge University Press
20070111
284
N/A
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