Spectral Methods for Time-Dependent Problems
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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Numerical analysis > Spectral Methods for Time-Dependent Problems: (Series Number 21 Cambridge Monographs on Applied and Computational Mathematics)
Spectral Methods for Time-Dependent Problems: (Series Number 21 Cambridge Monographs on Applied and Computational Mathematics)

Spectral Methods for Time-Dependent Problems: (Series Number 21 Cambridge Monographs on Applied and Computational Mathematics)


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About the Book

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.

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.

About the Author :
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.

Review :
'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


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Product Details
  • ISBN-13: 9780521792110
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Height: 229 mm
  • No of Pages: 284
  • Returnable: N
  • Series Title: Series Number 21 Cambridge Monographs on Applied and Computational Mathematics
  • Weight: 639 gr
  • ISBN-10: 0521792118
  • Publisher Date: 11 Jan 2007
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Returnable: N
  • Spine Width: 19 mm
  • Width: 152 mm


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Spectral Methods for Time-Dependent Problems: (Series Number 21 Cambridge Monographs on Applied and Computational Mathematics)
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