Spectral approach to D-bar problems
Numerical Analysis
2015-08-11 v1 Exactly Solvable and Integrable Systems
Abstract
We present the first numerical approach to D-bar problems having spectral convergence for real analytic rapidly decreasing potentials. The proposed method starts from a formulation of the problem in terms of an integral equation which is solved with Fourier techniques. The singular integrand is regularized analytically. The resulting integral equation is approximated via a discrete system which is solved with Krylov methods. As an example, the D-bar problem for the Davey-Stewartson II equations is solved. The result is used to test direct numerical solutions of the PDE.
Cite
@article{arxiv.1508.02363,
title = {Spectral approach to D-bar problems},
author = {C. Klein and K. McLaughlin},
journal= {arXiv preprint arXiv:1508.02363},
year = {2015}
}