Strang Splitting Methods for a quasilinear Schrödinger equation - Convergence, Instability and Dynamics

Abstract

We study the Strang splitting scheme for quasilinear Schrödinger equations. We establish the convergence of the scheme for solutions with small initial data. We analyze the linear instability of the numerical scheme, which explains the numerical blow-up of large data solutions and connects to analytical breakdown of regularity of solutions to quasilinear Schrödinger equations. Numerical tests are performed for a modified version of the superfluid thin film equation.

25 pages, 7 figures, References Updated, Figures added, Computations Extended and Material Re-organized, Additional Comments from Anonymous Referees incorporated, corrected convergence proof to address a loss of regularity due to a comment from L. Gauckler