Spectral Approach to D-bar Problems

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 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.
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Contributeur : Imb - Université de Bourgogne <>
Soumis le : mercredi 5 juillet 2017 - 12:00:16
Dernière modification le : vendredi 8 juin 2018 - 14:50:07

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Christian Klein, Kenneth D. Mclaughlin. Spectral Approach to D-bar Problems. Communications on Pure and Applied Mathematics, Wiley, 2017, 70 (6), pp.1052 - 1083. ⟨10.1002/cpa.21684⟩. ⟨hal-01556588⟩



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