By John P. Boyd

Thoroughly revised textual content specializes in use of spectral easy methods to clear up boundary price, eigenvalue, and time-dependent difficulties, but additionally covers Hermite, Laguerre, rational Chebyshev, sinc, and round harmonic capabilities, in addition to cardinal features, linear eigenvalue difficulties, matrix-solving tools, coordinate adjustments, equipment for unbounded periods, round and cylindrical geometry, and masses extra. 7 Appendices. thesaurus. Bibliography. Index. Over one hundred sixty textual content figures.

**Read Online or Download Chebyshev and Fourier spectral methods PDF**

**Similar functional analysis books**

**A panorama of harmonic analysis**

Tracing a course from the earliest beginnings of Fourier sequence via to the newest learn A landscape of Harmonic research discusses Fourier sequence of 1 and several other variables, the Fourier remodel, round harmonics, fractional integrals, and singular integrals on Euclidean house. The climax is a attention of rules from the perspective of areas of homogeneous variety, which culminates in a dialogue of wavelets.

This publication introduces most crucial points of recent research: the idea of degree and integration and the idea of Banach and Hilbert areas. it truly is designed to function a textual content for first-year graduate scholars who're already conversant in a few research as given in a ebook just like Apostol's Mathematical research.

**Lineare Funktionalanalysis: Eine anwendungsorientierte Einführung**

Die lineare Funktionalanalysis ist ein Teilgebiet der Mathematik, das Algebra mit Topologie und research verbindet. Das Buch führt in das Fachgebiet ein, dabei bezieht es sich auf Anwendungen in Mathematik und Physik. Neben den vollständigen Beweisen aller mathematischen Sätze enthält der Band zahlreiche Aufgaben, meist mit Lösungen.

- Theory and Applications of Volterra Operators in Hilbert Space
- Analysis IV: Integration and Spectral Theory, Harmonic Analysis, the Garden of Modular Delights (Universitext)
- Pseudo-differential operators: Complex analysis and partial differential equations
- Volterra Equations
- Applied Pseudoanalytic Function Theory (Frontiers in Mathematics)
- Student's Guide to Calculus by J. Marsden and A. Weinstein (Vol 3)

**Additional resources for Chebyshev and Fourier spectral methods**

**Sample text**

LOCATION OF SINGULARITIES 39 condition which is spatially periodic and antisymmetric with respect to both the origin and x = π. 43) where the sign function equals one when its argument is positive and is equal to minus one when its argument is negative. 13 shows the initial condition (Eq. 42) and its second derivative. The latter has jump discontinuities at x = ±0, π, 2 π, . . At t = 0, these discontinuities cause no problems for a Chebyshev expansion because the Chebyshev series is restricted to x ∈ [0, π] (using Chebyshev polynomials with argument y ≡ (2/π)(x − π/2)).

The reason is that the timedependence can be marched forward, from one time level to another. Marching is much cheaper than computing the solution simultaneously over all space-time. A space-only spectral discretization reduces the original partial differential equation to a set of ordinary differential equations in time, which can then be integrated by one’s favorite Runge-Kutta or other ODE time-marching scheme. 28) with the boundary conditions that the solution must be periodic with a period of 2π.

The series with only the constant and the cosine terms is known as a “Fourier cosine series”. ) If f (x) = −f (−x) for all x, then f (x) is said to be antisymmetric about x = 0 and all the an = 0. Its Fourier series is a sine series. These special cases are extremely important in applications as discussed in the Chapter 8. 2. 6) f (x) = f (x + 2π) for all x. To illustrate these abstract concepts, we will look at four explicit examples. These will allow us to develop an important theme: The smoother the function, more rapidly its spectral coefficients converge.