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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
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
- 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.
- 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
- S. Olver (2009), Computing the Hilbert transform and its inverse, to appear in Maths Comp.
- S. Olver (2009), Fast, numerically stable computation of oscillatory integrals with stationary points, to appear in BIT.
- S. Olver (2010), Shifted GMRES for oscillatory integrals, Numer. Math. 114: 607–628.
- S. Olver (2009), GMRES for the differentiation operator, SIAM J. Numer. Anal. 47: 3359–3373.
- S. Olver (2009), On the convergence rate of a modified Fourier series, Maths 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
Miscellaneous
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