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

The quadrature and asymptotics of highly oscillatory integrals, in both univariate and multivariate domains. Function approximation with polyharmonic series. Krylov subspace methods for oscillatory differential equations. Computing the Hilbert transform. Numerical solution of Riemann–Hilbert problems.

Preprints

S. Olver (2009), "Computing the Hilbert transform and its inverse", Report no. NA-09/7, Computing Laboratory, Oxford University, submitted on 10 Nov 2009.
S. Olver (2009), "GMRES for oscillatory matrix-valued differential equations", Report no. NA-09/3, Computing Laboratory, Oxford University, submitted to a conference proceeding on 17 Sept 2009.
S. Olver (2009), "Fast, numerically stable computation of oscillatory integrals with stationary points", Report no. NA-09/2, Computing Laboratory, Oxford University, submitted on 5 May 2009.

Papers

S. Olver (2008), "Shifted GMRES for oscillatory integrals", to appear in Numer. Math.
S. Olver (2008), "GMRES for the differentiation operator", to appear in SIAM J. Numer. Anal.
S. Olver (2009), "On the convergence rate of a modified Fourier series", Math. Comp. 78: 1629–1645.
S. Olver (2007), "Moment-free numerical approximation of highly oscillatory integrals with stationary points", Euro. J. Appl. Maths 18: 435–447.
S. Olver (2007), "Numerical approximation of vector-valued highly oscillatory integrals", BIT, 47: 637–655.
S. Olver (2006), "On the quadrature of multivariate highly oscillatory integrals over non-polytope domains", Numer. Math. 103: 643–665.
S. Olver (2006), "Moment-free numerical integration of highly oscillatory functions", IMA J. Numer. Anal. 26: 213–227.

Essays

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

Book Chapters

D. Huybrechs & S. Olver (2009), "Highly oscillatory quadrature", Highly Oscillatory Problems, London Mathematical Society Lecture Note Series 366, Cambridge University Press.
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

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.
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.