Mini-Course: Introduction to Spectral Methods

Speaker: Professor Wang Li-Lian (Nanyang Technological University, Singapore)

Time: 14:30-16:30, July 27^th, Monday

08:30-10:30, July 28^th, Tuesday

14:30-16:30, July 28^th, Tuesday

Venue: 5107, the 5^th Teaching Building

Contents:

1. Spectral bases from eigenvalue problems

• Fourier and generalised Fourier bases from Laplace eigenvalue problems

• Singular Sturm-Liouville problems and orthogonal systems

• Fundamental approximation theory

2. Fourisation and polynomial-based spectral methods

• The notion of “Fourisation” in spectral methods

• Some algorithms and analysis of Legendre and Chebyshev spectral methods

• Legendre spectral collocation method and its preconditioning