Download Chebyshev and Fourier Spectral Methods, Second Edition by John P. Boyd PDF

By John P. Boyd

Thoroughly revised textual content makes a speciality of use of spectral the right way to remedy boundary worth, eigenvalue, and time-dependent difficulties, but in addition covers Hermite, Laguerre, rational Chebyshev, sinc, and round harmonic services, in addition to cardinal services, linear eigenvalue difficulties, matrix-solving tools, coordinate variations, round and cylindrical geometry, and extra. comprises 7 appendices and over one hundred sixty textual content figures.

Show description

Read or Download Chebyshev and Fourier Spectral Methods, Second Edition PDF

Best functional analysis books

Classical complex analysis

Textual content at the idea of capabilities of 1 complicated variable comprises, with many embellishments, the topic of the classes and seminars provided by way of the writer over a interval of forty years, and may be thought of a resource from which a number of classes might be drawn. as well as the fundamental subject matters within the cl

Commensurabilities among Lattices in PU (1,n).

The 1st a part of this monograph is dedicated to a characterization of hypergeometric-like capabilities, that's, twists of hypergeometric features in n-variables. those are handled as an (n+1) dimensional vector area of multivalued in the neighborhood holomorphic features outlined at the house of n+3 tuples of designated issues at the projective line P modulo, the diagonal part of car P=m.

The gamma function

This short monograph at the gamma functionality used to be designed by way of the writer to fill what he perceived as a niche within the literature of arithmetic, which regularly taken care of the gamma functionality in a way he defined as either sketchy and overly advanced. writer Emil Artin, one of many 20th century's prime mathematicians, wrote in his Preface to this publication, "I consider that this monograph may also help to teach that the gamma functionality should be considered one of many straight forward services, and that every one of its uncomplicated houses will be tested utilizing hassle-free equipment of the calculus.

Topics in Fourier Analysis and Function Spaces

Covers numerous periods of Besov-Hardy-Sobolevtype functionality areas at the Euclidean n-space and at the n-forms, specifically periodic, weighted, anisotropic areas, in addition to areas with dominating mixed-smoothness houses. in keeping with the most recent options of Fourier research; the ebook is an up-to-date, revised, and prolonged model of Fourier research and features areas by means of Hans Triebel.

Extra resources for Chebyshev and Fourier Spectral Methods, Second Edition

Example text

It is for this reason that our series, instead of being the more familiar Taylor expansions, will be Fourier or Chebyshev or Legendre series instead. If its disk of convergence is too small to include the boundaries, the power series will give nonsense. In contrast, the success of spectral methods is guaranteed as long as the target interval, x ∈ [−1, 1], is free of singularities. 8 Stalking the Wild Singularity or Where the Branch Points Are It is sometimes possible to identify the type and nature of the singularities of the solution to a differential equation a priori without knowing the solution.

6 Darboux’s Principle Theorem 1 (DARBOUX’S PRINCIPLE: SINGULARITIES & CONVERGENCE) For all types of spectral expansions (and for ordinary power series), both the DOMAIN of CONVER GENCE in the complex plane and also the RATE of CONVERGENCE are controlled by the LOCATION and STRENGTH of the GRAVEST SINGULARITY in the complex plane. “Singularity” in this context denotes poles, fractional powers, logarithms and other branch points, and discontinuities of f (z) or any of its derivatives. Each such singularity gives its own additive contribution to the coefficients an in the asymptotic limit n → ∞.

Historically, the “non–interpolating” methods were developed first. For this reason, the label “spectral” is sometimes used in a narrow sense as a collective tag for the “non– interpolating” methods. In these notes, we shall use “spectral” only as catch–all for global expansion methods in general, but the reader should be aware of its other, narrower usage. ). Many spectral models of time-dependent hydrodynamics split the calculation into several subproblems and apply different techniques to different subproblems.

Download PDF sample

Rated 4.70 of 5 – based on 9 votes