Shen, Jie.
Spectral Methods Algorithms, Analysis and Applications / [electronic resource] : 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
10.1007/978-3-540-71041-7 doi
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 / [electronic resource] : 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
10.1007/978-3-540-71041-7 doi
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