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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