Orthogonal rational functions on a semi-infinite interval
Journal of Computational Physics
Spectral methods using rational basis functions on an infinite interval
Journal of Computational Physics
Journal of Scientific Computing
Spectral methods and mappings for evolution equations on the infinite line
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
The Hermite spectral method for Gaussian-type functions
SIAM Journal on Scientific Computing
The discrete ordinate/pseudo-spectral method: review and application from a physicist's perspective
Australian Journal of Physics
A MATLAB differentiation matrix suite
ACM Transactions on Mathematical Software (TOMS)
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Rational scaled generalized Laguerre function collocation method for solving the Blasius equation
Journal of Computational and Applied Mathematics
The spectral methods for parabolic Volterra integro-differential equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Rational Chebyshev series for the Thomas-Fermi function: Endpoint singularities and spectral methods
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Laguerre collocation solutions to boundary layer type problems
Numerical Algorithms
Applied Numerical Mathematics
Hi-index | 31.47 |
The Fourier-sine-with-mapping pseudospectral algorithm of Fattal et al. [Phys. Rev. E 53 (1996) 1217] has been applied in several quantum physics problems. Here, we compare it with pseudospectral methods using Laguerre functions and rational Chebyshev functions. We show that Laguerre and Chebyshev expansions are better suited for solving problems in the interval r ∈ [0, ∞] (for example, the Coulomb-Schrödinger equation), than the Fourier-sinemapping scheme. All three methods give similar accuracy for the hydrogen atom when the scaling parameter L is optimum, but the Laguerre and Chebyshev methods are less sensitive to variations in L. We introduce a new variant of rational Chebyshev functions which has a more uniform spacing of grid points for large r, and gives somewhat better results than the rational Chebyshev functions of Boyd [J. Comp. Phys. 70 (1987) 63].