A Riemann-Hilbert approach to the computation of transform pairs

@misc{lilly2026riemannhilbert,
  title = {{A Riemann-Hilbert approach to the computation of transform pairs}},
  author = {Kaitlynn Lilly and Thomas Trogdon},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.25252},
  eprint = {2606.25252},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.25252},
}

TY  - UNPB
TI  - A Riemann-Hilbert approach to the computation of transform pairs
AU  - Kaitlynn Lilly
AU  - Thomas Trogdon
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2606.25252
UR  - https://arxiv.org/abs/2606.25252
AB  - 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.
ER  -