Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Uniform asymptotic expansions for prolate spheriodal functions with large parameters
SIAM Journal on Mathematical Analysis
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
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
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Journal of Computational Physics
Spectral methods in MatLab
A MATLAB differentiation matrix suite
ACM Transactions on Mathematical Software (TOMS)
Parallel algorithms with local Fourier basis
Journal of Computational Physics
A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds
Journal of Computational Physics
Accuracy, Resolution, and Stability Properties of a Modified Chebyshev Method
SIAM Journal on Scientific Computing
Nonlinear Optimization, Quadrature, and Interpolation
SIAM Journal on Optimization
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
Semi-Implicit Spectral Element Atmospheric Model
Journal of Scientific Computing
Parallel Implementation Issues: Global versus Local Methods
Computing in Science and Engineering
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,
Spectral Methods Based on Prolate Spheroidal Wave Functions for Hyperbolic PDEs
SIAM Journal on Numerical Analysis
ACM Transactions on Mathematical Software (TOMS)
Hybrid Eulerian-Lagrangian Semi-Implicit Time-Integrators
Computers & Mathematics with Applications
A Hybrid Fourier---Chebyshev Method for Partial Differential Equations
Journal of Scientific Computing
Spectral analysis of the finite Hankel transform and circular prolate spheroidal wave functions
Journal of Computational and Applied Mathematics
Effective band-limited extrapolation relying on Slepian series and l1 regularization
Computers & Mathematics with Applications
A Prolate-Element Method for Nonlinear PDEs on the Sphere
Journal of Scientific Computing
The EPS method: A new method for constructing pseudospectral derivative operators
Journal of Computational Physics
The Nonconvergence of $$h$$h-Refinement in Prolate Elements
Journal of Scientific Computing
Hi-index | 31.45 |
Prolate spheroidal functions of order zero are generalizations of Legendre polynomials which, when the "bandwidth parameter" c 0, oscillate more uniformly on x ∈ [-1,1] than either Chebyshev or Legendre polynomials. This suggests that, compared to these polynomials, prolate functions give more uniform spatial resolution. Further, when used as the spatial discretization for time-dependent partial differential equations in combination with explicit time-marching, prolate functions allow a longer stable timestep than Legendre polynomials. We show that these advantages are real and further, that it is almost trivial to modify existing pseudospectral and spectral element codes to use the prolate basis. However, improvements in spatial resolution are at most a factor of π/2, approached slowly as N → ∞ The timestep can be lengthened by several times, but not by a factor that grows rapidly with N. The prolate basis is not likely to radically expand the range of problems that can be done on a workstation. However, for production runs on the "bleeding edge" edge of arithmurgy, such as numerical weather prediction, the rewards for switching to a prolate basis may be considerable.