Spectral Methods for Time-Dependent Problems

Jan S. Hesthaven

ISBN 10: 0521792118 / ISBN 13: 9780521792110

Published by Cambridge University Press, 2007

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9780521792110

Bibliographic Details

• Title: Spectral Methods for Time-Dependent Problems
• Publisher: Cambridge University Press
• Publication Date: 2007
• Language: English
• ISBN 10: 0521792118
• ISBN 13: 9780521792110
• Binding: Buch
• Condition: Neu
• Dimensions: 235W x 157H x 21D millimeters 235 millimeters width by 157 millimeters height by 21 millimeters depth
• Weight: 615 grams

About this title

Synopsis

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.

About the Authors

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.