31 citations · 35 across the 7 of their papers we have counts for
8 papers
Summation-by-parts operators for general function spaces: optimal nodes
Nicholas Hale, Charis Harley, Prince Nchupang +1
Gauss-Lobatto quadrature nodes and weights are optimal for closed summation-by-parts (SBP) formulations based on polynomial approximation spaces in the sense that for a prescribed…
Construction of Laguerre pseudospectral differentiation matrices
Emma Nel, Nicholas Hale
In this paper, we present a stable and efficient approach for constructing Laguerre pseudospectral differentiation matrices. The proposed method reformulates the off-diagonal entri…
Prandtl's extended mixing length model applied to the two-dimensional turbulent classical far wake
AJ Hutchinson, N Hale, K Born +1
Despite its limitations, Prandtl's mixing length model is widely applied in modelling turbulent free shear flows. Prandtl's extended model addresses many of the shortfalls of the o…
The ultraspherical spectral element method
Daniel Fortunato, Nicholas Hale, Alex Townsend
We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincaré-Steklov scheme for solving second-order linear partial differ…
Hedging and Pricing European-type, Early-Exercise and Discrete Barrier Options using Algorithm for the Convolution of Legendre Series
Tat Lung Chan, Nicholas Hale
This paper applies an algorithm for the convolution of compactly supported Legendre series (the CONLeg method) (cf. Hale and Townsend 2014a), to pricing/hedging European-type, earl…
An ultraspherical spectral method for linear Fredholm and Volterra integro-differential equations of convolution type
Nicholas Hale
The Legendre-based ultraspherical spectral method for ordinary differential equations is combined with a formula for the convolution of two Legendre series to produce a new techniq…
A fast and spectrally convergent algorithm for rational-order fractional integral and differential equations
Nicholas Hale, Sheehan Olver
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The…
A fast FFT-based discrete Legendre transform
Nicholas Hale, Alex Townsend
An algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast tr…