Presented by:
Sheehan Olver Imperial College London
Date:
Friday 9th August 2019 - 12:00 to 13:15
Venue:
INI Seminar Room 1
Abstract:
Orthogonal
polynomials are fundamental tools in numerical methods, including for singular
integral equations. A known result is that Cauchy transforms of weighted
orthogonal polynomials satisfy the same three-term recurrences as the
orthogonal polynomials themselves for n > 0. This basic fact leads to
extremely effective schemes of calculating singular integrals and
discretisations of singular integral equations that converge spectrally fast
(faster than any algebraic power). Applications considered include matrix Riemann–Hilbert
problems on contours consisting of interconnected line segments and Wiener–Hopf
problems. This technique is extendible to calculating singular integrals with
logarithmic kernels, with applications to Green’s function reduction of PDEs
such as the Helmholtz equation.
Using novel change-of-variable formulae, we will adapt these results to tackle singular integral equations on more general smooth arcs, geometries with corners, and Wiener–Hopf problems whose solutions only decay algebraically.
Using novel change-of-variable formulae, we will adapt these results to tackle singular integral equations on more general smooth arcs, geometries with corners, and Wiener–Hopf problems whose solutions only decay algebraically.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
