Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan–Shepp ridge polynomials, Chebyshev–Fourier Series, cylindrical Robert functions, Bessel–Fourier expansions, square-to-disk conformal mapping and radial basis functions

Author:

Boyd John P.,Yu Fu

Funder

National Science Foundation

Undergraduate Research Opportunities Program (UROP)

Publisher

Elsevier BV

Subject

Computer Science Applications,Physics and Astronomy (miscellaneous),Applied Mathematics,Computational Mathematics,Modeling and Simulation,Numerical Analysis

Reference107 articles.

1. Handbook of Mathematical Functions;Abramowitz,1965

2. O.S. Adams, Elliptic functions applied to conformal world maps, Special Publication 112, US Coast and Geodetic Survey, Washington, DC, available as PDF from the National Oceanic and Atmospheric Administration, 1925, p. 113.

3. Solving the Helmholtz equation for membranes of arbitrary shape: numerical results;Amore;J. Phys. A: Math. Theor.,2008

4. A spectral method for elliptic equations: the Dirichlet problem;Atkinson;Adv. Comput. Math.,2010

5. K. Atkinson, D. Chien, O. Hansen, A spectral method for elliptic equations: the Neumann problem, (submitted for publication).

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