Spectral Approach to D-bar Problems

Christian Klein, Kenneth D. T-R McLaughlin

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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 that is numerically solved with Fourier techniques. The singular integrand is regularized analytically. The resulting integral equation is approximated via a discrete system that is solved with Krylov methods. As an example, the D-bar problem for the Davey-Stewartson II equations is considered. The result is used to test direct numerical solutions of the PDE.

Original languageEnglish (US)
Pages (from-to)1052-1083
Number of pages32
JournalCommunications on Pure and Applied Mathematics
Issue number6
StatePublished - Jun 2017

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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