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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > On the numerical solution of Riemann--Hilbert problems with theta-function asymptotics

## On the numerical solution of Riemann--Hilbert problems with theta-function asymptoticsAdd to your list(s) Download to your calendar using vCal - Thomas Trogdon (University of Washington)
- Tuesday 25 July 2023, 11:30-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. CATW04 - Complex analysis: techniques, applications and computations - perspectives in 2023 We consider the numerical solution of Riemann—Hilbert problems that are asymptotically posed on a union of disjoint intervals. The singularities present in the solution of the problem are captured accurately using singular weight functions. A collocation method using orthogonal polynomials with respect to these weights is developed. The primary applications we discuss are to (1) the numerical solution of the computation of the finite-genus solutions of the KdV equation and to (2) the computation of the three-term recurrence coefficients for polynomials orthogonal on multiple intervals. With regard to (1), we give a new numerical method to solve the periodic initial-value problem for the KdV equation and compute large-genus solutions. For (2), an outcome of the work is a new implementation of inner-product free iterative solvers for indefinite linear systems. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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