My research is in numerical analysis and computational methods. I have developed spectral methods for ordinary and partial differential equations, singular integral equations, and Riemann–Hilbert problems, with applications in integrable systems and the study of random matrices.
Olver S, Xu Y, Non-homogeneous wave equation on a cone, Integral Transforms and Special Functions, ISSN:1065-2469
Snowball B, Olver S, 2020, Sparse spectral and p-finite element methods for partial differential equations on disk slices and trapeziums, Studies in Applied Mathematics, Vol:145, ISSN:0022-2526, Pages:3-35
Gutleb T, Olver S, 2020, A sparse spectral method for Volterra integral equations using orthogonal polynomials on the triangle, Siam Journal on Numerical Analysis, Vol:58, ISSN:0036-1429, Pages:1993-2018
Olver S, Xu Y, Orthogonal polynomials in and on a quadratic surface of revolution, Mathematics of Computation, ISSN:0025-5718
Olver S, Xu Y, Orthogonal structure on a quadratic curve, Ima Journal of Numerical Analysis, ISSN:0272-4979