Low regularity exponential-type integrators for nonlinear Schrödinger equations

Supervisor
Alexander Ostermann - Universität Innsbruck
Date and time
Wednesday, May 3, 2017 at 4:30 PM - Rinfresco 16.15, inizio seminario 16.30.
Place
Ca' Vignal - Piramide, Floor 0, Hall Verde
Programme Director
External reference
Publication date
April 18, 2017
Department
Computer Science  

Summary

Nonlinear Schrödinger equations are usually solved by pseudo-spectral methods where the time integration is performed by splitting schemes or exponential integrators. Notwithstanding the benefits of this approach, its successful application requires additional regularity of the solution. In this talk, we introduce as an alternative low regularity exponential-type integrators.

For such methods, first-order convergence only requires the boundedness of one additional derivative of the solution. This allows us to impose lower regularity assumptions on the data than for instance required for classical splitting or exponential integration schemes. For one dimensional quadratic Schrödinger equations we can even prove first-order convergence without any loss of regularity. Numerical experiments underline the favorable error behavior of the newly introduced exponential-type integrators for low regularity solutions compared to classical splitting and exponential integration schemes.

Contact Person: Marco Caliari





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