Projects in Applied Mathematics (MATH3422/4422)

Numerical analysis of spectral methods:

This project is about a class of numerical methods, called spectral methods, whereby the approximate solution of a differential equation is represented by an expansion in trial functions (typically trigonometric, Chebyshev or Legendre polynomials). Spectral methods have been applied with tremendous success in a wide range of research areas, particularly in fluid mechanics, meteorology and turbulence theory; their strength lies in the exponential convergence of the approximate expansion for problems with a smooth solution.
This project could, for instance, focus on (1) the analysis of the stability and convergence properties of spectral methods; (2) the treatment of non-smooth or aliased solutions; (3) the spectral element method (i.e. piecewise spectral method).
Some knowledge of numerical analysis (e.g. MATH2600, MATH3474) and some knowledge of functional analysis (e.g. MATH2375, MATH2431 or MATH3215) would be an advantage to undertake this project.

References:
Spectral methods for time-dependent problems by J.S. Hesthaven, S. Gottlieb & D. Gottlied (Cambridge University Press, 2007)
Spectral methods. Fundamentals in single domains by C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang (Springer, 2006)
Chebyshev and Fourier spectral methods by J.P. Boyd (Dover Publisher, 2000)

Interested candidates should contact Evy Kersalé.
(email: kersale@maths.leeds.ac.uk - phone: 0113 343 5180)