Spectral Methods
Shen, Jie.
Spectral Methods Algorithms, Analysis and Applications / [recurso electrónico] : by Jie Shen, Tao Tang, Li-Lian Wang. - XVI, 472 p. online resource. - Springer Series in Computational Mathematics, 41 0179-3632 ; . - Springer Series in Computational Mathematics, 41 .
Introduction -- Fourier Spectral Methods for Periodic Problems -- Orthogonol Polynomials and Related Approximation Results -- Second-Order Two-Point Boundary Value Problems -- Integral Equations -- High-Order Differential Equations -- Problems in Unbounded Domains -- Multi-Dimensional Domains -- Mathematical Preliminaries -- Basic iterative methods -- Basic time discretization schemes -- Instructions for routines in Matlab. .
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 to help the readers to develop their own spectral codes for their specific applications.
9783540710417
Mathematics.
Computer science.
Differential equations, partial.
Computer science--Mathematics.
Mathematics.
Computational Mathematics and Numerical Analysis.
Partial Differential Equations.
Mathematics of Computing.
QA71-90
518 518
Spectral Methods Algorithms, Analysis and Applications / [recurso electrónico] : by Jie Shen, Tao Tang, Li-Lian Wang. - XVI, 472 p. online resource. - Springer Series in Computational Mathematics, 41 0179-3632 ; . - Springer Series in Computational Mathematics, 41 .
Introduction -- Fourier Spectral Methods for Periodic Problems -- Orthogonol Polynomials and Related Approximation Results -- Second-Order Two-Point Boundary Value Problems -- Integral Equations -- High-Order Differential Equations -- Problems in Unbounded Domains -- Multi-Dimensional Domains -- Mathematical Preliminaries -- Basic iterative methods -- Basic time discretization schemes -- Instructions for routines in Matlab. .
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 to help the readers to develop their own spectral codes for their specific applications.
9783540710417
Mathematics.
Computer science.
Differential equations, partial.
Computer science--Mathematics.
Mathematics.
Computational Mathematics and Numerical Analysis.
Partial Differential Equations.
Mathematics of Computing.
QA71-90
518 518
