An ODE--based approach to some Riemann--Hilbert problems motivated by wave diffraction
Analysis of PDEs
2012-10-09 v1 Classical Analysis and ODEs
Complex Variables
Abstract
A novel approach to Riemann--Hilbert problems of particular class is introduced. The approach is applicable to problems in which the multiplicative jump is set on a half-line. Such problems are linked to some Wiener--Hopf problems motivated by diffraction theory. The new approach is based on ordinary differential equations: the Riemann--Hilbert problem is reduced to finding a coefficient of an ordinary differential equation and solving this equation. The new method leads to an efficient numerical algorithm and opens a road to new asymptotical and analytical advances.
Cite
@article{arxiv.1210.1964,
title = {An ODE--based approach to some Riemann--Hilbert problems motivated by wave diffraction},
author = {Andrey V. Shanin},
journal= {arXiv preprint arXiv:1210.1964},
year = {2012}
}
Comments
17 pages, 7 figures