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arXiv · 2606.25252

A Riemann-Hilbert approach to the computation of transform pairs

Kaitlynn Lilly·Thomas Trogdon
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Abstract

We develop a unified methodology that integrates spectral theory, Riemann-Hilbert problems, and inverse scattering theory for the construction and numerical evaluation of transform pairs associated with linear variable-coefficient partial differential equations. The approach combines analytical formulae with numerical methods for ordinary differential equations and Riemann-Hilbert problems, yielding a hybrid analytical-numerical strategy for working with these transforms. Results are presented for transforms arising in the Dirac equation, demonstrating accurate computations, even in the presence of discontinuous coefficients.

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Kaitlynn Lilly, Thomas Trogdon. 2026-06-24. A Riemann-Hilbert approach to the computation of transform pairs. https://arxiv.org/abs/2606.25252

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