Publications
62 results found
Vasil GM, Burns KJ, Lecoanet D, et al., 2016, Tensor calculus in polar coordinates using Jacobi polynomials, Journal of Computational Physics, Vol: 325, Pages: 53-73, ISSN: 0021-9991
Bornemann F, Its A, Olver S, et al., 2016, Numerical methods for the discrete map Z<sup>a</sup>, Advances in Discrete Differential Geometry, Pages: 151-176, ISBN: 9783662504468
As a basic example in nonlinear theories of discrete complex analysis, we explore various numerical methods for the accurate evaluation of the discrete map Za introduced by Agafonov and Bobenko. The methods are based either on a discrete Painlevé equation or on the Riemann-Hilbert method. In the latter case, the underlying structure of a triangular Riemann-Hilbert problem with a non-triangular solution requires special care in the numerical approach. Complexity and numerical stability are discussed, the results are illustrated by numerical examples.
Townsend A, Trogdon T, Olver S, 2016, Fast computation of Gauss quadrature nodes and weights on the whole real line, IMA JOURNAL OF NUMERICAL ANALYSIS, Vol: 36, Pages: 337-358, ISSN: 0272-4979
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- Citations: 28
Trogdon T, Olver S, 2016, A Riemann-Hilbert approach to Jacobi operators and Gaussian quadrature, IMA JOURNAL OF NUMERICAL ANALYSIS, Vol: 36, Pages: 174-196, ISSN: 0272-4979
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- Citations: 4
Trogdon T, Olver S, 2015, Riemann–Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions, Publisher: Society for Industrial and Applied Mathematics, ISBN: 9781611974195
Townsend A, Olver S, 2015, The automatic solution of partial differential equations using a global spectral method, Journal of Computational Physics
Olver S, Nadakuditi RR, Trogdon T, 2015, Sampling unitary ensembles, RANDOM MATRICES-THEORY AND APPLICATIONS, Vol: 4, ISSN: 2010-3263
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- Citations: 7
Slevinsky RM, Olver S, 2015, ON THE USE OF CONFORMAL MAPS FOR THE ACCELERATION OF CONVERGENCE OF THE TRAPEZOIDAL RULE AND SINC NUMERICAL METHODS, SIAM JOURNAL ON SCIENTIFIC COMPUTING, Vol: 37, Pages: A676-A700, ISSN: 1064-8275
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- Citations: 6
Deift PA, Menon G, Olver S, et al., 2014, Universality in numerical computations with random data, PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, Vol: 111, Pages: 14973-14978, ISSN: 0027-8424
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- Citations: 17
Olver S, Trogdon T, 2014, Nonlinear Steepest Descent and Numerical Solution of Riemann-Hilbert Problems, COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, Vol: 67, Pages: 1353-1389, ISSN: 0010-3640
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- Citations: 19
Olver S, 2014, Change of variable formulas for regularizing slowly decaying and oscillatory Cauchy and Hilbert transforms, ANALYSIS AND APPLICATIONS, Vol: 12, Pages: 369-384, ISSN: 0219-5305
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- Citations: 4
Olver S, Trogdon T, 2014, Numerical Solution of Riemann-Hilbert Problems: Random Matrix Theory and Orthogonal Polynomials, CONSTRUCTIVE APPROXIMATION, Vol: 39, Pages: 101-149, ISSN: 0176-4276
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- Citations: 13
Olver S, Townsend A, 2014, A practical framework for infinite-dimensional linear algebra, 1st First Workshop High Performance Technical Computing Dynamic Languages Held, Publisher: IEEE, Pages: 57-62
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- Citations: 25
Trogdon T, Olver S, 2013, Numerical inverse scattering for the focusing and defocusing nonlinear Schrodinger equations, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 469, ISSN: 1364-5021
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- Citations: 24
Olver S, Townsend A, 2013, A Fast and Well-Conditioned Spectral Method, SIAM REVIEW, Vol: 55, Pages: 462-489, ISSN: 0036-1445
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- Citations: 132
Olver S, 2012, A general framework for solving Riemann-Hilbert problems numerically, NUMERISCHE MATHEMATIK, Vol: 122, Pages: 305-340, ISSN: 0029-599X
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- Citations: 38
Trogdon T, Olver S, Deconinck B, 2012, Numerical inverse scattering for the Korteweg-de Vries and modified Korteweg-de Vries equations, PHYSICA D-NONLINEAR PHENOMENA, Vol: 241, Pages: 1003-1025, ISSN: 0167-2789
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- Citations: 35
Huybrechs D, Olver S, 2012, Superinterpolation in Highly Oscillatory Quadrature, FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, Vol: 12, Pages: 203-228, ISSN: 1615-3375
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- Citations: 28
Olver S, 2011, Computation of equilibrium measures, JOURNAL OF APPROXIMATION THEORY, Vol: 163, Pages: 1185-1207, ISSN: 0021-9045
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- Citations: 14
Olver S, 2011, COMPUTING THE HILBERT TRANSFORM AND ITS INVERSE, MATHEMATICS OF COMPUTATION, Vol: 80, Pages: 1745-1767, ISSN: 0025-5718
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- Citations: 32
Olver S, 2011, Erratum to: Numerical Solution of Riemann-Hilbert Problems: Painlevé II(Found Comput Math, 10.1007/s10208-010-9079-8), Foundations of Computational Mathematics, Vol: 11, ISSN: 1615-3375
Olver S, 2011, Numerical Solution of Riemann-Hilbert Problems: Painlev, II, FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, Vol: 11, Pages: 153-179, ISSN: 1615-3375
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- Citations: 31
Olver S, 2011, GMRES for oscillatory matrix-valued differential equations, Pages: 267-274, ISBN: 9783642153365
We investigate the use of Krylov subspace methods to solve linear, oscillatory ODEs. When we apply a Krylov subspace method to a properly formulated equation, we retain the asymptotic accuracy of the asymptotic expansion whilst converging to the exact solution. We demonstrate the effectiveness of this method by computing error and Mathieu functions. © 2011 Springer.
Olver S, 2010, Fast, numerically stable computation of oscillatory integrals with stationary points, BIT NUMERICAL MATHEMATICS, Vol: 50, Pages: 149-171, ISSN: 0006-3835
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- Citations: 33
Olver S, 2010, Shifted GMRES for oscillatory integrals, NUMERISCHE MATHEMATIK, Vol: 114, Pages: 607-628, ISSN: 0029-599X
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- Citations: 17
Olver S, 2009, ON THE CONVERGENCE RATE OF A MODIFIED FOURIER SERIES, MATHEMATICS OF COMPUTATION, Vol: 78, Pages: 1629-1645, ISSN: 0025-5718
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- Citations: 18
Olver S, 2009, GMRES FOR THE DIFFERENTIATION OPERATOR, SIAM JOURNAL ON NUMERICAL ANALYSIS, Vol: 47, Pages: 3359-3373, ISSN: 0036-1429
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- Citations: 15
Olver S, 2007, Numerical approximation of vector-valued highly oscillatory integrals, BIT NUMERICAL MATHEMATICS, Vol: 47, Pages: 637-655, ISSN: 0006-3835
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- Citations: 41
Olver S, 2007, Moment-free numerical approximation of highly oscillatory integrals with stationary points, EUROPEAN JOURNAL OF APPLIED MATHEMATICS, Vol: 18, Pages: 435-447, ISSN: 0956-7925
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- Citations: 49
Olver S, 2006, On the quadrature of multivariate highly oscillatory integrals over non-polytope domains, NUMERISCHE MATHEMATIK, Vol: 103, Pages: 643-665, ISSN: 0029-599X
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- Citations: 23
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