Sheehan Olver

Junior Research Fellow

St John's College
Oxford University
St Giles
Oxford OX1 3JP
United Kingdom

and

Mathematical Institute
24-29 St Giles'
Oxford OX1 3LB
United Kingdom

Telephone	+44 1865 273890
Email	Sheehan.Olver@sjc.ox.ac.uk

Research Interests

• Oscillatory differential equations: The quadrature and asymptotics of highly oscillatory integrals, in both univariate and multivariate domains. Krylov subspace methods for oscillatory differential equations. Modulated Fourier series for nonlinear ODEs with intrinsic oscillations.
• Numerical Riemann–Hilbert problems: Computing the Hilbert transform. Numerical solution of Riemann–Hilbert problems. Computing Painlevé transcendentals. Numerical nonlinear steepest descent.

Preprints

1. S. Olver (2009), Numerical solution of Riemann–Hilbert problems: Painlevé II, Report no. NA-09/9, Mathematical Institute, Oxford University, submitted on 21 Dec 2009.
2. S. Olver (2009), GMRES for oscillatory matrix-valued differential equations, Report no. NA-09/3, Mathematical Institute, Oxford University, submitted to a conference proceeding on 17 Sept 2009.

Papers

1. S. Olver (2009), Computing the Hilbert transform and its inverse, to appear in Maths Comp.
2. S. Olver (2009), Fast, numerically stable computation of oscillatory integrals with stationary points, to appear in BIT.
3. S. Olver (2010), Shifted GMRES for oscillatory integrals, Numer. Math. 114: 607–628.
4. S. Olver (2009), GMRES for the differentiation operator, SIAM J. Numer. Anal. 47: 3359–3373.
5. S. Olver (2009), On the convergence rate of a modified Fourier series, Maths Comp. 78: 1629–1645.
6. S. Olver (2007), Moment-free numerical approximation of highly oscillatory integrals with stationary points, Euro. J. Appl. Maths 18: 435–447.
7. S. Olver (2007), Numerical approximation of vector-valued highly oscillatory integrals, BIT, 47: 637–655.
8. S. Olver (2006), On the quadrature of multivariate highly oscillatory integrals over non-polytope domains, Numer. Math. 103: 643–665.
9. S. Olver (2006), Moment-free numerical integration of highly oscillatory functions, IMA J. Numer. Anal. 26: 213–227.

Essays

1. S. Olver (2008) Numerical Approximation of Highly Oscillatory Integrals, PhD Thesis, University of Cambridge.
2. S. Olver (2006) Numerical approximation of highly oscillatory integrals, Smith-Knight/Rayleigh-Knight Essay, Class 1.

Book Chapters

1. D. Huybrechs & S. Olver (2009), Highly oscillatory quadrature, Highly Oscillatory Problems, London Mathematical Society Lecture Note Series 366, Cambridge University Press.
2. D. Huybrechs & S. Olver (2009), Rapid function approximation by modified Fourier series, Highly Oscillatory Problems, London Mathematical Society Lecture Note Series 366, Cambridge University Press.

Proceedings

1. S. Olver (2007), Numerical quadrature of highly oscillatory integrals using derivatives, Algorithms for Approximation, A. Iske and J. Levesley (eds.), Springer-Verlag, Heidelberg, pp. 381-388.
2. A. Iserles, S. P. Nørsett & S. Olver (2006), Highly oscillatory quadrature: The story so far, Proceedings of ENuMath, Santiago de Compostela, A. Bermudez de Castro et al, (eds.), Springer-Verlag, Berlin, 97-118.

Presentations

• S. Olver, Numerically approximation of highly oscillatory integrals, Leslie Fox Second Prize Talk.

Miscellaneous

• S. Olver, Computer Modern fonts in Mathematica on Mac OS X.