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Nonlinear Schrödinger equations with nontrivial boundary conditions : analysis, applications and numerics (2010)

Organizers: PF Jean-Claude Saut (U. Paris Sud), PF Avy Soffer (U. Rutgers), Hans-Peter Stimming (WPI c/o Uni Wien) Mechthild Thalhammer (U.Innsbruck)

Talks


Gauckler, Ludwig (U.Tübingen) WPI, Seminar room C 714 Thu, 3. Mar 11, 11:45
"Convergence of a split-step Hermite method for the Gross-Pitaevskii equation"
The Gross-Pitaevskii equation is a nonlinear Schroedinger equation used to describe Bose-Einstein condensates. In this talk, we discuss a discretization of the Gross-Pitaevskii equation by Strang splitting in time and Hermite collocation in space. We prove a second order error bound for the semi- discretization in time by the Strang under suitable regularity assumptions on the exact solution. For the semi-discretization in space we show high order convergence, depending on the regularity of the exact solution. The analyses of the semi-discretizations in time and space are combined into an error analysis of the fully discrete method.
  • Thematic program: Nonlinear Schrödinger equations with nontrivial boundary conditions : analysis, applications and numerics (2010)

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