Spectral and Pseudospectral Methods

Fourier and Chebyshev expansions for PDE.


field tier

Spectral and Pseudospectral Methods. Fourier and Chebyshev expansions for PDE.

Foundations and canonical references

The standard treatments of spectral and pseudospectral methods approach the subject from complementary angles. Trefethen, Spectral Methods in MATLAB (2000) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Canuto, Spectral Methods: Fundamentals in Single Domains (2006) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for spectral and pseudospectral methods include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2000
    Spectral Methods in MATLAB
    trefethen-2000
  • textbook · primary · 2006
    Spectral Methods: Fundamentals in Single Domains
    canuto-2006, hussaini-2006, quarteroni-2006, zang-2006

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