Spectral and Pseudospectral Methods
Fourier and Chebyshev expansions for PDE.
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 · 2000Spectral Methods in MATLABtrefethen-2000
- textbook · primary · 2006Spectral Methods: Fundamentals in Single Domainscanuto-2006, hussaini-2006, quarteroni-2006, zang-2006
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