Spectral Methods: Algorithms, Analysis and Applications

Authors:
Jie Shen;Tao Tang;Li-Lian Wang
Affiliations:
-;-;-
Venue:
Spectral Methods: Algorithms, Analysis and Applications
Year:
2011

Citing 0
Cited 14

An efficient and stable spectral method for electromagnetic scattering from a layered periodic structure

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Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications

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Convergence Analysis of Spectral Galerkin Methods for Volterra Type Integral Equations

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Spectral collocation methods for Volterra-integro differential equations with noncompact kernels

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A GPU parallelized spectral method for elliptic equations in rectangular domains

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A spectral method for parabolic differential equations

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Application of the collocation method for solving nonlinear fractional integro-differential equations

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Generalized Hermite Approximations and Spectral Method for Partial Differential Equations in Multiple Dimensions

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A new triangular spectral element method I: implementation and analysis on a triangle

Numerical Algorithms
Laguerre collocation solutions to boundary layer type problems

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A Spectral-Element Method for Transmission Eigenvalue Problems

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An efficient spectral method for computing dynamics of rotating two-component Bose-Einstein condensates via coordinate transformation

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Jacobian-predictor-corrector approach for fractional differential equations

Advances in Computational Mathematics
Spectral Collocation Methods for Differential-Algebraic Equations with Arbitrary Index

Journal of Scientific Computing

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Abstract

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online tohelp the readers to develop their own spectral codes for their specific applications.