• Prandtl's extended mixing length model applied to the two-dimensional turbulent classical far wake
  AJ Hutchinson, N Hale, K Born, and DP Mason
  Proceedings of the Royal Society A, 2021
  Link: http://arxiv.org/abs/2101.08550
• The ultraspherical spectral element method
  D Fortunato, N Hale, A Townsend
  Journal of Computational Physics, 2021
  Link: https://arxiv.org/abs/2006.08756
• Pricing European-type, early-exercise and discrete barrier options using an algorithm for the convolution of Legendre series
  Tat Lung Chan, Nicholas Hale
  Quantitative Finance, 2020
  Link: https://www.tandfonline.com/doi/abs/10.1080/14697688.2020.1736612
  DOI: https://doi.org/10.1080/14697688.2020.1736612
• Quadratic Padé Approximation: Numerical Aspects and Applications
  M Fasondini, N Hale, R Spoerer, and JACW Weideman
  Computer Research and Modeling, 2019
  Link: (Free access)
  DOI: https://doi.org/10.20537/2076-7633-2019-11-6-1017-1031
• An ultraspherical spectral method for linear Fredholm and Volterra integro-differential equations of convolution type
  Nicholas Hale
  IMA Journal of Numerical Analysis, 2018
  Link: https://arxiv.org/abs/1712.00304
  DOI: https://doi.org/10.1093/imanum/dry042
• A fast and spectrally convergent algorithm for rational-order fractional integral and differential equations
  Nicholas Hale and Sheehan Olver
  SIAM Journal of Scientific Computing, 2018
  Link: HaleOlver2018.pdf
  DOI: https://doi.org/10.1137/16M1104901
• Contour integral solution of elliptic PDEs in cylindrical domains
  Nicholas Hale and JAC Weideman
  SIAM Journal of Scientific Computing, 2015
  Link: HaleWeideman2015.pdf
  DOI: http://dx.doi.org/10.1137/15M1032764
• A fast FFT-based discrete Legendre transform
  Nicholas Hale and Alex Townsend
  IMA Journal of Numerical Analysis, 2015
  Link: HaleTownsend2015.pdf
  DOI: http://dx.doi.org/10.1093/imanum/drv060
• Explicit construction of rectangular differentiation matrices
  Kuan Xu and Nicholas Hale
  IMA Journal of Numerical Analysis, 2015
  Link: (Free access)
  DOI: http://dx.doi.org/10.1093/imanum/drv013
  Errata: XuHale2015Errata.txt
• Rectangular spectral collocation
  Tobin Driscoll and Nicholas Hale
  IMA Journal of Numerical Analysis, 2015;
  doi: 10.1093/imanum/dru062
  Link: DriscollHale2015.pdf
  DOI: http://dx.doi.org/10.1093/imanum/dru062
• Chebfun Guide (1st edition)
  Tobin Driscoll, Nicholas Hale, and Lloyd N. Trefethen
  Pafnuty Publications, Oxford, (2014)
  Link: chebfun_guide.pdf
  
• An algorithm for the convolution of Legendre series
  Nicholas Hale and Alex Townsend
  SIAM Journal on Scientific Computing, 2014.
  Link: HaleTownsend2014b.pdf
  DOI: http://dx.doi.org/10.1137/140955835
• A fast, simple, and stable Chebyshev-Legendre transform using an asymptotic formula
  Nicholas Hale and Alex Townsend
  SIAM Journal on Scientific Computing, 2014.
  Link: HaleTownsend2014a.pdf
  DOI: http://dx.doi.org/10.1137/130932223
• Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights
  Nicholas Hale and Alex Townsend
  SIAM Journal on Scientific Computing, 2013.
  Link: HaleTownsend2013a.pdf
  DOI: http://dx.doi.org/10.1137/120889873
• Chebfun and Numerical Quadrature
  Nicholas Hale and Lloyd N. Trefethen
  Science in China, 2012.
  Link: HaleTrefethen2012.pdf
  DOI: http://dx.doi.org/10.1007/s11425-012-4474-z
  
• An Efficient Implementation of an Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
  Kevin Burrage, Nicholas Hale, and David Kay
  SIAM Journal on Scientific Computing, 2012.
  Link: BurrageHaleKay2012.pdf
  DOI: http://dx.doi.org/10.1137/110847007
• Convection and Heat Transfer in Layered Sloping, Warm-Water Aquifers
  Robert McKibbin, Nicholas Hale, Robert W. Style, and Nicole Walters
  Journal of Porous Media, 2011.
  DOI: http://dx.doi.org/10.1615/JPorMedia.v14.i4
• On The Use Of Conformal Maps To Speed Up Numerical Computations
  Nicholas Hale
  University of Oxford DPhil Thesis, 2009.
  Link: HaleThesis2009.pdf
  
• Conformal Maps to Multiply-Slit Domains and Applications
  Nicholas Hale and T. Wynn Tee
  SIAM Journal on Scientific Computing, 2009.
  Link: HaleTee2009.pdf
  DOI: http://dx.doi.org/10.1137/080738325
• Computing A^α, log(A), and Related Matrix Functions by Contour Integrals
  Nicholas Hale, Nicholas J. Higham, and Lloyd N. Trefethen
  SIAM Journal on Numerical Analysis, 2008.
  Link: HaleHighamTrefethen2008.pdf
  DOI: http://dx.doi.org/10.1137/070700607
• New Quadrature Methods From Conformal Maps
  Nicholas Hale and Lloyd N. Trefethen
  SIAM Journal on Numerical Analysis, 2008.
  Link: HaleTrefethen2008.pdf
  DOI: http://dx.doi.org/10.1137/07068607X
• A Sixth-Order Extension to the MATLAB Package bvp4c of J. Kierzenka and L. Shampine
  Nicholas Hale and Daniel R. Moore
  No. NA-08/04, Technical Report, Oxford University Computing Laboratory. 2008.
  Link: http://www.cs.ox.ac.uk/files/720/NA-08-04.pdf
  
• A Sixth-Order Extension to the MATLAB bvp4c Software of J. Kierzenka and L. Shampine.
  Nicholas Hale
  Imperial College London Masters Thesis. 2006.
  Link: Hale2006.pdf
  

Chebfun Examples

In addition, I have written a number of Chebfun Examples, a selection of which can be found below:

• The gamma function and its poles
  

  

• The Rosenbrock function in 2D optimisation (revisited)
  

  

• The Chebyshev-Legendre transform
  

  

• Spike integral
  

  

• The nullspace of a linear operator
  

  

• Resolution of wiggly functions
  

  

• Perimeter of an ellipse
  

  

• A periodic ODE system
  

  

• Convolution of probability distributions
  

  

• Padua points in Chebfun2
  

  

• Optimization of a parameterised integral
  

  

• The birthday paradox
  

  

• Orthogonal polynomials via the Gram-Schmidt process
  

  

• A keyhole contour integral