33 citations · 164 across the 51 of their papers we have counts for
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A Riemann--Hilbert approach to Jacobi operators and Gaussian quadrature
Thomas Trogdon, Sheehan Olver
The computation of the entries of Jacobi operators associated with orthogonal polynomials has important applications in numerical analysis. From truncating the operator to form a J…
On the application of GMRES to oscillatory singular integral equations
Thomas Trogdon
We present a new method for the numerical solution of singular integral equations on the real axis. The method's value stems from an explicit formula for the Cauchy integral of a c…
Dispersive and soliton perturbations of finite-genus solutions of the KdV equation: computational results
Thomas Trogdon, Bernard Deconinck
All solutions of the Korteweg -- de Vries equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytica…
A numerical dressing method for the nonlinear superposition of solutions of the KdV equation
Thomas Trogdon, Bernard Deconinck
In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg-de Vries (KdV) equation. The first method is used to so…