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
Sinc methods for quadrature and differential equations
Sinc methods for quadrature and differential equations
Computing the Hilbert transform on the real line
Mathematics of Computation
A spectral method for unbounded domains
Journal of Computational Physics
Shifted Chebyshev Collocation Domain Truncation for Solving Problems on an Infinite Interval
Journal of Scientific Computing
Near optimality of the sinc approximation
Mathematics of Computation
Hi-index | 7.29 |
In Part I we introduced the generalized Wiener rational basis functions, and here in Part II we continue our investigation with numerical experiments. Wiener's generalized basis can utilize the fast Fourier transform for integer values of the decay parameter s; we outline two algorithms for doing so. In addition, the issue of Galerkin representations for polynomial nonlinearities of expansions is addressed. The Wiener basis set is compared against domain truncation methods (Fourier and Chebyshev polynomials), Hermite functions, Sinc interpolations, and mapped Chebyshev expansions, and we show that for both exponentially and algebraically decaying functions, the Wiener approximation is as good as or superior to these alternatives. In addition, we carry out preliminary investigations regarding tuning of the decay parameter s. Numerical simulations of Korteweg-de Vries type equations show the effectiveness of the Wiener expansion. We also explore the practical use of the Wiener basis functions on the semi-infinite interval, which is compared against Laguerre function methods and other Jacobi polynomial mappings.