Spectral Methods In Matlab

Author: Lloyd N. Trefethen
Publisher: SIAM
ISBN: 9780898719598
Size: 23.65 MB
Format: PDF
View: 465

This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web.

Chebyshev And Fourier Spectral Methods

Author: John P. Boyd
Publisher: Courier Corporation
ISBN: 0486141926
Size: 39.53 MB
Format: PDF
View: 5917

Completely revised text applies spectral methods to boundary value, eigenvalue, and time-dependent problems, but also covers cardinal functions, matrix-solving methods, coordinate transformations, much more. Includes 7 appendices and over 160 text figures.

Introduction To Finite And Spectral Element Methods Using Matlab

Author: Constantine Pozrikidis
Publisher: CRC Press
ISBN: 142005709X
Size: 62.26 MB
Format: PDF
View: 6132

Why another book on the finite element method? There are currently more than 200 books in print with "Finite Element Method" in their titles. Many are devoted to special topics or emphasize error analysis and numerical accuracy. Others stick to the fundamentals and do little to describe the development and implementation of algorithms for solving real-world problems. Introduction to Finite and Spectral Element Methods Using MATLAB provides a means of quickly understanding both the theoretical foundation and practical implementation of the finite element method and its companion spectral element method. Written in the form of a self-contained course, it introduces the fundamentals on a need-to-know basis and emphasizes algorithm development and computer implementation of the essential procedures. Firmly asserting the importance of simultaneous practical experience when learning any numerical method, the author provides FSELIB: a software library of user-defined MATLAB functions and complete finite and spectral element codes. FSELIB is freely available for download from http://dehesa.freeshell.org, which is also a host for the book, providing further information, links to resources, and FSELIB updates. The presentation is suitable for both self-study and formal course work, and its state-of-the-art review of the field make it equally valuable as a professional reference. With this book as a guide, you immediately will be able to run the codes as given and graphically display solutions to a wide variety of problems in heat transfer and solid, fluid, and structural mechanics.

Approximation Theory And Approximation Practice

Author: Lloyd N. Trefethen
Publisher: SIAM
ISBN: 9781611972405
Size: 34.39 MB
Format: PDF, Kindle
View: 1896

An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.

Spectral Methods

Author: Jie Shen
Publisher: Springer Science & Business Media
ISBN: 3540710418
Size: 41.80 MB
Format: PDF
View: 6419

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.

Finite Difference Methods For Ordinary And Partial Differential Equations

Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Size: 22.48 MB
Format: PDF, ePub, Docs
View: 4161

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Spectra And Pseudospectra

Author: Lloyd Nicholas Trefethen
Publisher: Princeton University Press
ISBN: 9780691119465
Size: 39.10 MB
Format: PDF, Kindle
View: 3065

Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.

Kernel Based Approximation Methods Using Matlab

Author: Gregory Fasshauer
Publisher: World Scientific Publishing Company
ISBN: 9814630152
Size: 64.38 MB
Format: PDF, ePub, Mobi
View: 6462

In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.

Spectral Numerical Weather Prediction Models

Author: Martin Ehrendorfer
Publisher: SIAM
ISBN: 1611971985
Size: 55.42 MB
Format: PDF
View: 625

An explanation of the theory behind the spectral method and its application to building numerical weather prediction models.

Applied Asymptotic Analysis

Author: Peter David Miller
Publisher: American Mathematical Soc.
ISBN: 0821840789
Size: 35.69 MB
Format: PDF, Docs
View: 2385

"The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects."--BOOK JACKET.